Question

Find the linear polynomial in x which when divided by (x-3) leaves 6 as remainder and is exactly divisible by (x+3).

Answer 1

Let the linear polynomial be $p\left(x\right)=ax+b$

Given $p\left(3\right)=6$ and $p(-3)=0$

$a\left(3\right)+b=6$ and $a(-3)+b=0$

$3a+b=6$ and $-3a+b=0$

Solving these equations,

$b=3$ and $a=1$

Thus, the required linear polynomial is $x+3$.