Question

Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following:
$f(x)= 4x^{3} +8x + 8x^{2} +7,g(x)=2x^{2}-x+1$

Answer 1

SOLUTION IS IN THE ATTACHMENT…  

DIVISION ALGORITHM for polynomials :  

If f(x) and g(x) are any two polynomials with g(x) ≠0 , then we can find polynomials q(x) and r(x) , such that  

f(x) = g(x)  × q(x) + r(x)

Dividend =  Divisor ×  Quotient + Remainder

Where, r(x) = 0 or degree of r(x) < degree of g(x)  

This result is known as a division algorithm for polynomials.

★★ If r(x) = 0, then  polynomials g(x) is a factor of polynomial f(x) .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hey mate
refer to attachment