I need help for this If the polynomial 6x^4+8x^3+17x^2+21x+7 is divided by another polynomial 3x^2+4x+1 , - Maths - Polynomials

Question

I need help for this 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'

Ayush Jha · Accepted Answer

Here the quotient wil be ${c x}^{2} + d x + e$ as the difference of degrees of dividend and divisor is 2.

Now , Euclid's division lemma

Dividend = Divisor x Quotient + Remainder

$6 x^{4} + 8 x^{3} + 17 x^{2} + 21 x + 7 = (3 x^{2} + 4 x + 1) (c x^{2} + d x + e) + (a x + b)$

Comparing both the side we get,

6 = 3c

c = 2

Again,

3d+4c = 8

d = 0

Now,

3e+c+4d = 17

3e+2=17

e = 5

Now comparing the coefficients of x

4e+d+a=21

20+a=21

a=1

Comparing the constant term

e+b=7

5+b=7

b=2

I need help for this ... 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'.