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:
$f(x)= 15x^{3} -20x^{2} + 13x-12,g(x)=2-2x+x^{2}$

Answer 1

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Answer 2

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) .

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