Question

Determine which of the following polynomials have $(x+2)$ as a factor:

• A. $x^3+x^2+x+4$
• B. $x^3+x^2+x+5$
• C. $x^3+x^2+x+6$
• D. $x^3+x^2+x+7$

Answer 1

The correct option is C

$x^3+x^2+x+6$

Let $p\left(x\right)=x^3+x^2+x+6$
Zero of (x+2) is −2

p(−2)=${(-2)}^3+{(-2)}^2-2+6=-8+4-2+6=0$

Therefore, by the Factor Theorem, $(x+2)$ is the factor of $x^3+x^2+x+6$