Question

If $p\left(x\right)=x^3-5x^2+4x-3$ and $g\left(x\right)=x-2$, show that p(x) is not multiple of g(x).

Answer 1

$p\left(x\right)=x^3-5x^2+4x-3$ and $g\left(x\right)=x-2x=2$

If p(x) is not a multiple of g(x), the remainder will be a non-zero value.

$p\left(2\right)=2^3-5(2{)}^2+4(2)-3\Rightarrow p(2)=8-20+8-3\Rightarrow p(2)=16-23\Rightarrow p(2)=-7$

Therefore p(x) is not a multiple of g(x)