# How do you factor completely P(x)=x^4+4x^3-7x^2-34x-24?

Dec 12, 2016

$P \left(x\right) = \left(x + 1\right) \left(x + 2\right) \left(x + 4\right) \left(x - 3\right)$

#### Explanation:

The number of changes in signs of the coefficients of $P \left(\pm x\right)$ are1

and 1 and 3 respectively. So, the number of real roots is (0+0) 0 or

(1+1) 2 or (1+3).

The sum of the coefficients in P(-x) is 0. So, -1 is a zero of P.

The graph reveals zeros near x = -4, -2,-1 and 3.

Easily, P(-2) = P(-4) = P(3) = 0.

And so,

$P \left(x\right) = \left(x + 1\right) \left(x + 2\right) \left(x + 4\right) \left(x - 3\right)$

graph{y-x^4-4x^3+7x^2+34x+24=0 [-5, 5, -2.5, 2.5]}