Question

If the polynomial $6x^4+8x^3+17x^2+21x+7$ is divided by another polynomial $3x^2+4x+1$, the remainder comes out to be $ax+b$, find a and b.
[4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let us divide the polynomial $f\left(x\right)=6x^4+8x^3+17x^2+21x+7$ by the polynomial $g\left(x\right)=3x^2+4x+1$



Clearly, remainder $=x+2$

It is given that the remainder is $ax+b$

$ax+b=x+2$

$\Rightarrow a=1,b=2$ [On comparing the coefficients of like powers of x]