Question

What is the value of $p$ for which the polynomial $x^3+4x^2-px-6$ is completely divisible by $(x-1)$.

Answer 1

Polynomial $x^3+4x^2-px-6$

If divisible by $(x-1)$

Then at $x=1$ , value of polynomial should be zero

$(1{)}^3+4(1{)}^2-p\left(1\right)-6=0$

$⟹1+4-p-6=0$

$⟹p=-1$