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lyzzy7
 2 years ago
Which number makes this equation true?
v^2 + 10v + 16 = (v + 8)(v + ?)
lyzzy7
 2 years ago
Which number makes this equation true? v^2 + 10v + 16 = (v + 8)(v + ?)

This Question is Closed

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0I know a shortcut... can I say it?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2if 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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.28*? has to equal 16 so basically 8p = 16 p = ???

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2where p is that answer

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2yep, you nailed it

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so v^2 + 10v + 16 = (v + 8)(v + ?) turns into v^2 + 10v + 16 = (v + 8)(v + 2)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1What is the factored form of x^2 + 6x + 8?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2find two numbers that a) multiply to 8 (last term) AND b) add to 6 (middle coefficient)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.12 and 4 . @jim_thompson5910

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2So 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

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1ohhh! @ParthKohli thanks :)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2So it's just a matter of finding those two numbers then writing it in the form (x+number1)(x+number2)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0I know that was sarcastic. _

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1hold on im thinking @jim_thompson5910

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.15 and 3?? @jim_thompson5910

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2you found the numbers already by saying 2 and 4 2+4 = 6 (middle coefficient) 2*4 = 8 (last term)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so 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)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1so it's (x + 4)(x + 2) ?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2go ahead and expand out (x+2)(x+4) you'll find that you'll get x^2 + 6x + 8 back again

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so essentially what you've done is gone in reverse of expanding (which was done in the previous problem)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1i mostly get what you're saying. i have one more if you're willing to help?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2correct, the order of the factors doesn't matter so (x+2)(x+4) is the same as (x+2)(x+4)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2i meant (x+2)(x+4) is the same as (x+4)(x+2)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2sure go for it

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1What is the factored form of x^2 – 7x + 12? and dont worry i knew what you meant lol

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2same idea, just different numbers

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2find two numbers that multiply to 12 AND add to 7

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so it factors to (x3)(x4)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2unfortunately this trick only works if the leading coefficient is 1, but it's still useful

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2that'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

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1okay 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?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2well it's actually the same type of problem, just worded differently

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2they want you to factor g^2  2g  24

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2what do you get when you do?

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1write me an equation then and let me solve it :)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2find me two numbers that multiply to 24 and add to 2 at the same time

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.26 plus 4 = 10 and it does NOT equal 2

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.16 and 4? 6*4= 24 6+4 = 2 i think lol

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2So g^2  2g  24 factors to (g6)(g+4)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2notice how g+4 is a factor

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2the other factor is g6

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2let'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?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2correct since Area = Length times Width

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so if you have some area expression and you factor it, you get (Length)*(Width) where length and width are the factors of the area

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2it only works for rectangles though

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1hb this one? What is the factored form of 4x^2 + 12x + 5?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ok now the leading coefficient isn't 1 anymore, so we can't use that trick (well not the whole thing anyways)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2but we can still use some of the trick

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2first multiply 4 (first coefficient) and 5 (last term) to get 4*5 = 20

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2now list two numbers that multiply to 20 AND add to 12 (middle coefficient)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so 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)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2hopefully factoring by grouping is a familiar term

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1so the final answer is (2x + 1)(2x + 5), right?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2hopefully you see how I got all that

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1okay, thanks :D and lol yeah mostly.

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1The 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?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2alright, just keep practicing and it'll make more sense

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.210*(15) = 150

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2find two numbers that multiply to 150 and they add to 19

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1why do you multiply 10 and 15?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2because I'm using the AC method for factoring this method starts out by multiplying the first and last coefficients

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2then you find two numbers that multiply to that result and add to the middle number

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1so the formula is ax^2 + bx + c right?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2that's a basic form of a quadratic, yes

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2you 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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so that's why they call it the ac method

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1I cant find the two numbers that multiply to 150 and add to 19..

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2there's a long list to check, but luckily there's a shortcut

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2have you heard of the quadratic formula before?

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1noo. 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.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ah i'm sry to hear that, at least she'll be gone and a (hopefully) better teacher will take over

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1yeah im going to a private school next year, sadly now i need to get a second job because its $6,000 a year.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2dang that's quite pricey

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2well 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)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1i know right, and okay shoot

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2the quadratic formula is \[\Large x = \frac{b\pm\sqrt{b^24ac}}{2a}\] does that formula look familiar?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ok 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)?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ok 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.

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1I 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...

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1like i cant even read it in my head let alone get it. i have a headache.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2alright, sorry jumped too far ahead

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1its not your fault. it just is ridiculous that something that complicated even exists. i hate this world.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2well much more complicated things exist (that even I don't understand), but that's what keeps things interesting

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2let's ignore the quadratic formula until you get more practice with it

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1soo 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.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2why not sleep then come back?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.210(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)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1because 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.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2i 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)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so 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

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1Got it. and the length is 5x+3 right?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so length = 5x + 3 (given) width = 2x  5 (just found this)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1ughhh now i have to solve two more, then ima sleep. thank you so much for the help!

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2go ahead and post and hopefully it won't take too long

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2then you can finally sleep (til you have to get up in the morning...ugh lol)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1you sure? i mean i could try to do them on my own if you want.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2sure whatever works best for you

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2how about you work them and I check what you get

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2or I can show you how if you're stuck

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1alright heres this one What is the factored form of 2x2 + x – 3? then i'll do the other.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ok 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)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2hopefully I didn't cut you off there?

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1no you're good, i was just going to say the two numbers. but how in god's name did you do that so fast....

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ah i should have let you say the two numbers, but hopefully you got 3 and 2 ?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2ok perfect, you'll be a pro in no time

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2you just need to practice more with factoring by grouping (and the quadratic formula when you get more time)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1and 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?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2no, you're not almost right....you're absolutely correct (lol I wanted to sound like a game show host for a sec)

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1OMG YAY:))) Thank you sooo much! like i really didnt get half my stuff till you helped lol

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2glad to be of help, now get some sleep lol

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2I know, I probably sound like your mom, but idc lol

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1your good lol! how old are u by the way?

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1lol nah its cool. and its amazing that you put your brain to help people. what do you do as a job?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2but thanks lol

lyzzy7
 2 years ago
Best ResponseYou've already chosen the best response.1i hope you go far! honestly

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2thanks, i hope so too

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2definitely getting a lot of practice here lol

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2and building networks as well (well sorta i guess)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2so that's another plus
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