Question

If $(x+2)$ and $(x+3)$ are factors of $x^3+ax+b$, find the value of 'a' and 'b'.

Answer 1

Given polynomial is $p\left(x\right)=x^3+ax+b$

$x+2$ is a factor $\Rightarrow$ $-2$ is a root of the polynomial.

$\Rightarrow (-2{)}^3+a(-2)+b=0\Rightarrow -2a+b=8$

$x+3$ is a factor $\Rightarrow -3$ is a root of the polynomial.

$\Rightarrow (-3{)}^3+a(-3)+b=0\Rightarrow -3a+b=27$

Solving the above equations, we get $a=-19,b=-30$