Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$p\left(x\right)=2x^3-7x^2+9x-13,g\left(x\right)=x-3$

Answer 1

$p\left(x\right)=2x^3-7x^2+9x-13g\left(x\right)=x-3$

By remainder theorem, when p(x) is divided by ( x − 3), then the remainder = p(3).
Putting x = 3 in p(x), we get

$\left(p\right(3)=2(3{)}^3-7(3{)}^2+9(3)-13=54-63+27-13=5$

∴ Remainder = 5

Thus, the remainder when p(x) is divided by g(x) is 5.