Question

y(x)= x^4-x^3-7x^2+x+6
Express y(x) in factored form. Consider using synthetic division

Answer 1

Since the last term is 6, you'd test 1,2,3,6,-6,-3,-2,-1

Answer 2

I just tested that y(3)=0

Answer 3

Synthetic divide it by 3

Answer 4

I just divided 3 and got 0. I'm not sure about my final answer after factoring though

Answer 5

So far I have (x+3)(x^3-2x^2-x-2)

Answer 6

Hmm, tested 1 and got 0 so \(x-1\) would be a factor.

Answer 7

Hmm, why \(x+3\)? \(-3\) is not a root.

Answer 8

I tried 1 and I'm not sure if I factored it right

Answer 9

What did you get?

Answer 10

Just to check your answer, see
http://www.wolframalpha.com/input/?i=factor+x^4-x^3-7x^2%2Bx%2B6+

Answer 11

Wolframalpha gave
\[
x^4-x^3-7 x^2+x+6=(x-3) (x-1) (x+1) (x+2)
\]