Question

Find the remainder when $x^3-a{x}^2+6x-a$ is divided by $x-a$.

Answer 1

Step 1: Determine the value of $x$ for the divisor

Given equation is $x^3-a{x}^2+6x-a$ which is divided by $x-a$.

Put divisor $x-a$$=0$

$\Rightarrow$ $x=a$

Step 2: Determine the Remainder

Consider the equation

$x^3-a{x}^2+6x-a$

By using Remainder theorem,

Putting $x=a$

$\therefore$Remainder is

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

$=a^3-a^3+6a-a$

$=5a$

Hence, remainder when $x^3-a{x}^2+6x-a$ is divided by $x-a$ is $5a$.