Question

If (x - a) is factor of the polynomial $x^3-m{x}^2-2nax+n{a}^2$ ; prove that a = m + n

Answer 1

The given polynomial is $x^3-m{x}^2-2nax+n{a}^2$

$x-a$ is a factor of that polynomial.

So, the value of polynomial will become zero if substitute $x=a$

$a^3-m{a}^2-2na\left(a\right)+n{a}^2=0$

$a^3-m{a}^2-2n{a}^2+n{a}^2=0$

$a^3-m{a}^2-n{a}^2=0$

$a^3=a^2(m+n)$

$\Rightarrow a=m+n$