Factor 3x⁴-17x³-12x²-62 x+20

- anonymous

Factor 3x⁴-17x³-12x²-62 x+20

- chestercat

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- anonymous

From my calculations, it's unfactorable. Is this a multiple choice answer?

- anonymous

It's not multiply choice. It is factorable, but into two quadratics. Those cannot be factor. All I'm asking is how do you factor this?

- anonymous

How do you factor 3x⁴-17x³-12x²-62 x+20 into two quadratics?

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## More answers

- anonymous

Link would be helpful too.

- anonymous

I get it. I know I have a video of this somewhere. One second.

- mathslover

Factor theorem will surely work.

- mathslover

find the factors of 20 first... can you tell me @micahwood50 ?

- anonymous

I'm not sure how to do this, can you show me?

- mathslover

what are the factors of 20?

- anonymous

1, 2, 4, 5, 10, 20

- mathslover

is -1 , -2 , -4,-5,-10, -20 also factors of 20 ?

- anonymous

Yeah.

- mathslover

so , now one by one put : \(\pm 1,\pm 2, \pm 4, \pm 5, \pm 10, \pm 20\) at the place of x in the given expression

- mathslover

In which you get the answer as 0 ?

- mathslover

3x⁴-17x³-12x²-62 x+20
for example : \(3(-1)^4 -17(-1)^3 -12(-1)^2 -62(-1)+20\)
\(-3 +17 -12 + 62 + 20 \)
\(84 \ne 0\)
Do like this for each : \(\pm 1,\pm 2, \pm 4, \pm 5, \pm 10, \pm 20\)

- mathslover

Can you do this @micahwood50 ?

- anonymous

Umm, I tried all of them, none of them works.

- anonymous

http://www.wolframalpha.com/input/?i=factor%283x%5E4-17x%5E3-12x%5E2-62x%2B20%29

- anonymous

those are only the rational roots

- mathslover

we want integral roots...

- anonymous

You know what? Save your time and help someone else. I'm googling Factor theorem. Thanks, though.

- anonymous

if the lowest terms with integer coefficients are quadratics, there aren't any.

- anonymous

factors, not terms

- anonymous

that wording was bad, but I think you know what I mean

- anonymous

\(\large 3x^4-17x^3-12x^2-62x+20 =(3x^2+4x+10)(x^2-7x+2)\)
"Link would be helpful too. "
I read a post about factoring into quadratics. Here is a post in which someone tried to explain the method of factoring into quadratics, but I could not understand it. :(
http://openstudy.com/users/dpainc#/updates/4fcfdafce4b0c6963adaf2bc

- anonymous

I don't think that that would apply in this situation, unless you could see that x^2 -7x + 2 is a factor.

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