Question

Form a cubic polynomial whose zeros are $-3,-1$ and $2$.

Answer 1

The given zeros are $-3,-1$ and $2$

So, the factors of the polynomial are $(x-(-3\left)\right),(x-(-1\left)\right)$ and $(x-2)$

Then the polynomial

$P\left(x\right)=(x-(-3\left)\right)(x-(-1\left)\right)(x-2)$

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

$=(x^2+4x+3)(x-2)$

$=x^3-2x^2+4x^2-8x+3x-6$

$=x^3+2x^2-5x-6$

Hence, the polynomial is $x^3+2x^2-5x-6$