Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$\left(px\right)=3x^4-6x^2-8x-2,g\left(x\right)=x-2$

Answer 1

$\left(px\right)=3x^4-6x^2-8x-2g\left(x\right)=x-2$

By remainder theorem, when p(x) is divided by ( x − 2), then the remainder = p(3).
Putting x = 2 in p(x), we get

$p\left(2\right)=3(2{)}^4-6(2{)}^2-8\left(2\right)-2=48-24-16-2=6$

∴ Remainder = 6

Thus, the remainder when p(x) is divided by g(x) is 6.