p(x)=x3+8x2−7x+12 and g(x)=x−1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remainder respectively. If a is the degree of q(x) and b is the degree of r(x), (a−b)=?.
A
1
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B
2
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C
3
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D
4
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Solution
The correct option is B 2 Remainder =r(x)=p(1)=13+8×12−7×1+12=14 The degree of a polynomial is the highest degree of its terms when the polynomial is expressed in its canonical form consisting of a linear combination of monomials. So, Degree of r(x)=b=0 q(x)=p(x)g(x) Now , p(x)=x3+8x2−7x+12 g(x)=(x−1) Performing long division