Question

Find all the other zeros of the polynomial $p\left(x\right)=2x^3+3x^2-11x-6$ if one of its zero is $-3$.

Answer 1

$p\left(x\right)=2x^3+3x^2-11x-6$

Since $x=-3$ is a zero of $p\left(x\right)$

So, by factor theorem $x+3$ is a factor of $p\left(x\right)$

Now, if we divide $2x^3+3x^2-11x-6$ by $x+3$, quotient is $2x^2-3x-2$ and remainder is $0$.

Therefore,

$2x^3+3x^2-11x=(x+3)(2x^2-3x-2)$

$=(x+3)(2x+1)(x-2)$

for other zeroes of $p\left(x\right)$

$2x+1=0,x-2=0$

Hence the other zeroes are $-\frac{1}{2},2$