Question

Given the polynomial P(x)=x^3-5x+10x-12, is x+3 a factor of P(x)? Explain why. Make sure to show work.

Answer 1

x + 3 is not a factor of the polynomial

Explanation:

Using the factor and remainder theorem, if the given expression is a factor, by substituting the value of the expression set to zero , then , we should have 0 as our remaining value after substituting

Set x + 3 to zero

x + 3 = 0

This means;

x = -3

so;

f(-3) = -3^3 -5(-3) + 10(-3) - 12

= -27 + 15 -30 -12

= -54

Since what we have is not equal to zero, then x + 3 is not a factor of the polynomial