Question

Please help me!!! I will give brainliest!!!! Is x + 9 a factor of the polynomial P(x) = x^3 + 11x^2 + 15x -27? If so, write the polynomial as a product of two factors. If not, explain how you know.

Answer 1

Answer:

Yes, it is a factor.

$p(x) = (x + 9)( {x}^{2} + 2x - 3)$

Step-by-step explanation:

Let us quickly perform a synthetic synthetic division to determine whether x+9 is a factor of

$p(x) = {x}^{3} + 11 {x}^{2} + 15x - 27$

We perform the synthetic division as shown in attachment.

Since the remainder is zero, x+9 is a factor of p(x).

From the results of our division, the quotient is :

$q(x) = {x}^{2} + 2x - 3$

Therefore the polynomial as a product of two factors is:

$p(x) = {x}^{3} + 11 {x}^{2} + 15x - 27 = (x + 9)( {x}^{2} + 2x - 3)$