6 + 10 x + 14 x^2
what's the GCF here and is it smaller than the smallest coefficient?

- anonymous

6 + 10 x + 14 x^2
what's the GCF here and is it smaller than the smallest coefficient?

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- amistre64

2 see it as GCF = 2

- amistre64

1,2,3,6 is the best you can get, what number do the rest have in common with this?

- anonymous

I'm thinking

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## More answers

- amistre64

....think....quieter.....

- anonymous

It hurts....

- anonymous

I am not sure...why do I not get this stuff?

- amistre64

tell me, what are the coeeficients?

- anonymous

2

- amistre64

2 is a coefficient?

- anonymous

I know whatever it is is not smaller then it is, because they are equal to each other...just not sure what number

- anonymous

it is 6?

- amistre64

6 is the smallest coefficient..yes; so any factors cannot possibly be larger than 6.

- anonymous

Thank you so much..sorry about any trouble I caused

- amistre64

think of it this way:
if someone wants you to give them $10 and all you have is $3; what is the most you can give them?

- anonymous

3

- amistre64

exactly; so, in this problem of yours we have some numbers that are carrying cash...
the largest amount of cash that they have in common cant be greater than the "$6" number right?

- anonymous

right

- amistre64

so lets open up that "$6" dollars wallet and see what hes got in there...
hes got the following bills:
$1, $2, $3 , $6. the rest of the numbers have similar types of cash. but the biggest numbered bill they have in common is a $2.

- anonymous

I get it....that sounds simple...till you get to the way it looks in front, if they would word the things like you just did, I would be fine...

- amistre64

the "10" is carrying:
$1, $2, $5, $10
the "14" is carrying:
$1, $2, $7, $14
the only "bills" they have in common are $2 bills

- anonymous

Maybe you can help me with the next 2 things, do you have time?

- anonymous

I wish you were my teacher.....

- amistre64

i got at most an hour and a half :)

- anonymous

only 2 small questions left....

- anonymous

what are the different ways a quadratic polynomial can be factored out. What applies when?

- anonymous

and..........
x ^ 3 + 2x^2 + x = 0
Can factorization still help solve this equation ? If yes, how ?

- anonymous

Those are it...If you have time.

- amistre64

lets dooooo this!!! ... :)

- amistre64

thats my machoman randy savage impersonation :)

- amistre64

what are the different ways a quadratic polynomial can be factored out. What applies when?
the different ways to factor a quad equation..... well, there is the trial and error method

- anonymous

I love your enthusiasm:)

- amistre64

lol

- anonymous

I think they should put a like button on here!lol

- amistre64

there is the "completeing the square" method

- amistre64

hah...i think thats the fan button. they give you cool titles like lifesaver, champion, star...but when you get to 100 and above, they turn you into a sandwich :/

- anonymous

:( (to the sandwich part) I'm a fan of you:)

- anonymous

I suck i have no fans

- amistre64

awww.... thanx :) I hit 200 a few days ago and was hoping for something cool like "turkey club on rye"..but noooooo.....they stuck me with "superhero" lol

- anonymous

be right back...I need to check on my daughters...

- anonymous

lol...

- anonymous

ok..they are fine

- amistre64

the four most used methods to factor quadratics are:
Factoring
Factor by Grouping
Quadratic Formula
Completing the Square

- anonymous

Does that have to do with the 1st question

- amistre64

When do we use them? dunno really.
Factoring is just splitting it up into its basic components... that can be done if its easy to recognize

- amistre64

yeah sure...maybe :)

- amistre64

by grouping generally ocuurs when there are more than 3 terms. we group them into pairs and factor them seperatley

- amistre64

the quad formula is used when we just dont have time or patience to do the other ways :)

- amistre64

and completing the square is just the long hand version of the quad formula, I guess you use it when you cant recall the quadratic formula :)

- anonymous

Now to the 2nd question

- amistre64

x ^ 3 + 2x^2 + x = 0
Can factorization still help solve this equation ? If yes, how ?
Yes, if we can notice that all the terms include an "x" factor then we can remove it and do our quadratic techniques on the remaining terms like this:
x ^ 3 + 2x^2 + x = 0
x(x^2 +2x +x) = 0
x (x+1)(x+1) = 0
x = 0 or x = -1

- amistre64

that little straggling +x should be a +1....

- amistre64

x(x^2 +2x +x) = 0 <- right in there
x(x^2 +2x +1) = 0
x (x+1)(x+1) = 0

- anonymous

ok, Now I am confused...

- anonymous

lol...story of my life

- amistre64

tell me whats got you confused :)

- anonymous

about the straggling....

- amistre64

I had a typo in there; that x^2 +2x +[x] <- right there.
it should have been: x^2 +2x +1

- anonymous

Thank you got it! I will probably be on again tomorrow.....I have this stuff all week and get really frustrated! Thanks for all your help! You are great! I am sure you are better then a sandwich:)

- amistre64

thanx :) take care ;)

- anonymous

You too

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