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Question

# Polynomials p(x),g(x),q(x) and r(x), which satisfy the division algorithm and "deg q(x)= deg r(x)", are

A
p(x)=2x2+x;g(x)=2x24;
q(x)=2x7;r(x)=x+2
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B
p(x)=x2+x3;g(x)=x2+x1;
q(x)=7;r(x)=5
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C
p(x)=x2+x;g(x)=x24;
q(x)=2x1;r(x)=x2
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D
p(x)=2x2+2x+8;g(x)=x2+x+9;
q(x)=2;r(x)=10
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Solution

## The correct option is B p(x)=2x2+2x+8;g(x)=x2+x+9;q(x)=2;r(x)=−10according to division algorithm p(x)=q(x)g(x)+r(x)degree of q(x) is equal to r(x) in all options.only (D) option satisfies p(x)=q(x)g(x)+r(x)g(x)q(x)=2(x2+x+9)=2x2+2x+18=p(x)+10=p(x)−r(x) hence p(x)=q(x)g(x)+r(x) in (D) satisfies division algorithm

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