Question

Divide: $2x^4+x^3+8x^2+14x+5$ by $(2x+1)$ (use division algorithm method).

Answer 1

Solution:

Let $p\left(x\right)=2x^4+x^3+8x^2+14x+5$

and $g\left(x\right)=2x+1$

Using Division Algorithm Method

$p\left(x\right)=q\left(x\right).g\left(x\right)+r\left(x\right)$

or, $p\left(x\right)=2x^4+x^3+8x^2+14x+5$

and $g\left(x\right)=2x+1$

then, $q\left(x\right)=x^3+4x+5$ and $r\left(x\right)=0$