Question

Write the polynomial in factored form:
X^3 + 7x^2 + 15x + 9

Answer 1

replace x by -1 and see what you get

Answer 2

If you get zero, this will imply that x+1 is a factor

Answer 3

You can divide by x+1 and obatain a quadratic that might be easier to factor

Answer 4

How do I do that? I'm confused because it's not a trinomial

Answer 5

Ahh, this relates to the Rational Root Theorem, I believe, yes?

Answer 6

If you divide your polynomial by x +1, you get
\[
\frac{x^3+7 x^2+15
x+9}{x+1}=x^2+6 x+9
\]

Answer 7

Can you factor
\[
x^2+6 x+9
\]

Answer 8

Yes it does

Answer 9

Notice that
\[
x^2+6 x+9=(x+3)^2
\]

Answer 10

I know how to factor that yea, I don't really get how you divide by x-1

Answer 11

So finally
\[
x^3+7 x^2+15 x+9=(x+1) (x+3)^2
\]

Answer 12

Use synthetic division

Answer 13

The way @eliassaab found -1 , @yankeeez , is by taking all the possible factors of the function where \( x= \pm \frac{p}{q}\) where p is the constant infront of \(x^3\) and \(q = 9\). This gives -1 as a possible candidate for factoring out the polynomial in preparation for reduction.

Answer 14

http://mathworld.wolfram.com/SyntheticDivision.html