Question

Determine whether $(x+1)$ is a factor of the polynomial:

$2x^4+9x^3+2x^2+10x+15$

Answer 1

According to factor theorem, when $f\left(x\right)$ is divided by $(x+1)$, $f(-1)=0$

$f\left(x\right)=2x^4+9x^3+2x^2+10x+15$

$f(-1)=2(-1{)}^4+9(-1{)}^3+2(-1{)}^2+10(-1)+15$

$=2-9+2-10+15=0$

$\because f(-1)=0,(x+1)$ is a factor of the given polynomial.