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Which number makes this equation true?
v^2 + 10v + 16 = (v + 8)(v + ?)
 one year ago
 one year ago
Which number makes this equation true? v^2 + 10v + 16 = (v + 8)(v + ?)
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.0
I know a shortcut... can I say it?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
if you were to set up a table, the lower right corner would have the value of 8*? where the answer would replace the question mark
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
8*? has to equal 16 so basically 8p = 16 p = ???
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
where p is that answer
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
yep, you nailed it
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so v^2 + 10v + 16 = (v + 8)(v + ?) turns into v^2 + 10v + 16 = (v + 8)(v + 2)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
What is the factored form of x^2 + 6x + 8?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
The shortcut says that in \(v^2 + \color{blue}{10}v + \rm something \) and \((v + \color{green}{a})(v + \color{green}{b})\), the sum of the greens is the blue guy.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
find two numbers that a) multiply to 8 (last term) AND b) add to 6 (middle coefficient)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
im confused @ParthKohli
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
2 and 4 . @jim_thompson5910
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
It's simple. You have \((v + 8)(v + ?)\). This shortcut says that \(8 + ? = 10\).
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
So x^2 + 6x + 8 factors to (x+2)(x+4) The rule is that x^2 + bx + c factors to (x+m)(x+n) where m+n = b and m*n = c
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
ohhh! @ParthKohli thanks :)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
So it's just a matter of finding those two numbers then writing it in the form (x+number1)(x+number2)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
I know that was sarcastic. _
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
hold on im thinking @jim_thompson5910
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
5 and 3?? @jim_thompson5910
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
you found the numbers already by saying 2 and 4 2+4 = 6 (middle coefficient) 2*4 = 8 (last term)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so because you found two numbers that multiply to 8 AND add to 6 the factorization of x^2 + 6x + 8 would be (x+2)(x+4)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
so it's (x + 4)(x + 2) ?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
go ahead and expand out (x+2)(x+4) you'll find that you'll get x^2 + 6x + 8 back again
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so essentially what you've done is gone in reverse of expanding (which was done in the previous problem)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
i mostly get what you're saying. i have one more if you're willing to help?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
correct, the order of the factors doesn't matter so (x+2)(x+4) is the same as (x+2)(x+4)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
i meant (x+2)(x+4) is the same as (x+4)(x+2)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
sure go for it
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
What is the factored form of x^2 – 7x + 12? and dont worry i knew what you meant lol
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
same idea, just different numbers
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
find two numbers that multiply to 12 AND add to 7
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so it factors to (x3)(x4)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
unfortunately this trick only works if the leading coefficient is 1, but it's still useful
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
that's the same as (x3)(x4) because the order of the factors does not matter ex: 2 time 3 = 6 and 3 times 2 = 6
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
okay i have a different kind of problem... The area of a garden is given by the trinomial g2 – 2g – 24. The garden’s length is g + 4. What is the garden’s width?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
well it's actually the same type of problem, just worded differently
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
they want you to factor g^2  2g  24
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
what do you get when you do?
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
write me an equation then and let me solve it :)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
find me two numbers that multiply to 24 and add to 2 at the same time
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
6 plus 4 = 10 and it does NOT equal 2
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
6 and 4? 6*4= 24 6+4 = 2 i think lol
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
So g^2  2g  24 factors to (g6)(g+4)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
notice how g+4 is a factor
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
the other factor is g6
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
let's go back to the question The area of a garden is given by the trinomial g2 – 2g – 24. The garden’s length is g + 4. What is the garden’s width?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
correct since Area = Length times Width
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so if you have some area expression and you factor it, you get (Length)*(Width) where length and width are the factors of the area
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
it only works for rectangles though
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
hb this one? What is the factored form of 4x^2 + 12x + 5?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ok now the leading coefficient isn't 1 anymore, so we can't use that trick (well not the whole thing anyways)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
but we can still use some of the trick
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
first multiply 4 (first coefficient) and 5 (last term) to get 4*5 = 20
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
now list two numbers that multiply to 20 AND add to 12 (middle coefficient)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
is it (4x + 5)(x + 1) ?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so we break 12x into 2x + 10x then we factor by grouping 4x^2+12x+5 4x^2+2x+10x+5 (4x^2+2x)+(10x+5) 2x(2x+1)+(10x+5) 2x(2x+1)+5(2x+1) (2x+5)(2x+1)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
hopefully factoring by grouping is a familiar term
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
so the final answer is (2x + 1)(2x + 5), right?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
hopefully you see how I got all that
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
okay, thanks :D and lol yeah mostly.
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
alright, just keep practicing and it'll make more sense
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
10*(15) = 150
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
find two numbers that multiply to 150 and they add to 19
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
why do you multiply 10 and 15?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
because I'm using the AC method for factoring this method starts out by multiplying the first and last coefficients
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
then you find two numbers that multiply to that result and add to the middle number
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
so the formula is ax^2 + bx + c right?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
that's a basic form of a quadratic, yes
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
you would multiply 'a' and 'c' to get a*c or just ac then you find two numbers that multiply to ac and add to b
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so that's why they call it the ac method
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
I cant find the two numbers that multiply to 150 and add to 19..
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
no you're not
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
there's a long list to check, but luckily there's a shortcut
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
have you heard of the quadratic formula before?
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
noo. my teacher sucks this year. she is retiring so she doesnt teach us anything useful, she just assigns stuff and tells us to read our book to figure out how to do it, but the book has no tips or tricks.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ah i'm sry to hear that, at least she'll be gone and a (hopefully) better teacher will take over
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
yeah im going to a private school next year, sadly now i need to get a second job because its $6,000 a year.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
dang that's quite pricey
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
well anyways, the quadratic formula isn't that bad to learn (it's a bit ugly the first time you see it, but once you get used to it, it's not so bad)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
i know right, and okay shoot
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
the quadratic formula is \[\Large x = \frac{b\pm\sqrt{b^24ac}}{2a}\] does that formula look familiar?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ok but does it look readable by that I mean, could you simplify that formula if you had to (or if you had to plug in numbers for a, b, and c)?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ok in this case, a = 10, b = 19 and c = 15 we plug those values into the formula to get this (there's a lot of steps, but just take things one step at a time) \[\Large x = \frac{b\pm\sqrt{b^24ac}}{2a}\] \[\Large x = \frac{(19)\pm\sqrt{(19)^24(10)(15)}}{2(10)}\] \[\Large x = \frac{19\pm\sqrt{361(600)}}{20}\] \[\Large x = \frac{19\pm\sqrt{361+600}}{20}\] \[\Large x = \frac{19\pm\sqrt{961}}{20}\] \[\Large x = \frac{19+\sqrt{961}}{20} \ \text{or} \ x = \frac{19\sqrt{961}}{20}\] \[\Large x = \frac{19+31}{20} \ \text{or} \ x = \frac{1931}{20}\] \[\Large x = \frac{50}{20} \ \text{or} \ x = \frac{12}{20}\] \[\Large x = \frac{5}{2} \ \text{or} \ x = \frac{3}{5}\] Let me know when you want to continue.
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
I honestly have no clue what any of that is. att all. like at all. im taking algebra 1 btw. im in 8th grade. but i really have cant even read that...
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
like i cant even read it in my head let alone get it. i have a headache.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
alright, sorry jumped too far ahead
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
its not your fault. it just is ridiculous that something that complicated even exists. i hate this world.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
well much more complicated things exist (that even I don't understand), but that's what keeps things interesting
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
let's ignore the quadratic formula until you get more practice with it
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
soo what is the answer to this? The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool? its like 5 am where i live and i still havent slept.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
why not sleep then come back?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
10(15) = 150 find two numbers that multiply to 150 and add to 19 ....do a bunch of trial and error guesses... you'll find that the two numbers are 6 and 25 So this means... 10x^219x15 10x^2+6x25x15 (10x^2+6x)+(25x15) 2x(5x+3)+(25x15) 2x(5x+3)5(5x+3) (2x5)(5x+3)  In short 10x^219x15 completely factors to (2x5)(5x+3)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
because the kind of person i am, when i have something on my mind, i have to get it done before i'd ever care for myself.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
i gotcha, that's both a good and bad trait because yes it's good to be this motivated, but not when you're sleep deprived (you won't learn much without a good night's sleep)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so anyways, back to the problem above I showed how 10x^219x15 factors to (2x5)(5x+3) 5x+3 was one factor we were already given, 2x5 is the other one So the width is 2x5
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
Got it. and the length is 5x+3 right?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so length = 5x + 3 (given) width = 2x  5 (just found this)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
ughhh now i have to solve two more, then ima sleep. thank you so much for the help!
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
go ahead and post and hopefully it won't take too long
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
then you can finally sleep (til you have to get up in the morning...ugh lol)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
you sure? i mean i could try to do them on my own if you want.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
sure whatever works best for you
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
how about you work them and I check what you get
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
or I can show you how if you're stuck
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
alright heres this one What is the factored form of 2x2 + x – 3? then i'll do the other.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ok 2(3) = 6 find two numbers that multiply to 6 and add to 1 those two numbers are 3 and 2 so... 2x^2+x3 2x^2+3x2x3 ... break 1x into 3x  2x, then factor by grouping (2x^2+3x)+(2x3) x(2x+3)+(2x3) x(2x+3)1(2x+3) (x1)(2x+3)  2x^2+x3 completely factors to (x1)(2x+3)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
hopefully I didn't cut you off there?
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
no you're good, i was just going to say the two numbers. but how in god's name did you do that so fast....
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ah i should have let you say the two numbers, but hopefully you got 3 and 2 ?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
ok perfect, you'll be a pro in no time
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
you just need to practice more with factoring by grouping (and the quadratic formula when you get more time)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
and for the other one it was What is the factored form of 3x2 + 21x – 24? and i got 3(x + 8)(x – 1) am i almost right?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
no, you're not almost right....you're absolutely correct (lol I wanted to sound like a game show host for a sec)
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
OMG YAY:))) Thank you sooo much! like i really didnt get half my stuff till you helped lol
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
glad to be of help, now get some sleep lol
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
I know, I probably sound like your mom, but idc lol
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
your good lol! how old are u by the way?
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
lol nah its cool. and its amazing that you put your brain to help people. what do you do as a job?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
but thanks lol
 one year ago

lyzzy7Best ResponseYou've already chosen the best response.1
i hope you go far! honestly
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
thanks, i hope so too
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
definitely getting a lot of practice here lol
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
and building networks as well (well sorta i guess)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.2
so that's another plus
 one year ago
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