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Question

Verify division algorithm for the polynomials f(x)=8+20x+x26x3 and g(x)=2+5x3x2.

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Solution

First, we write the given polynomials in standard form in decreasing order of degree and then perform the division as shown below.

f(x)=8+20x+x26x3
f(x)=6x3+x2+20x+8

g(x)=2+5x3x2
g(x)=3x2+5x+2
So

f(x)g(x)



r(x)=x+8

q(x)=2x+3

(Quotient×divisor)+remainder

=(2x+3)(3x2+5x+2)+x+2

=6x3+10x2+4x9x2+15x+6+x+2

Therefore, 6x3+x2+20x+8=dividend

Thus,(Quotient×divisor)+remainder=dividend

Hence, the division algorithm is verified


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