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When \( \Large x^{3}+2x^{2}+4x+b \) is divided by \( \Large x+1 \), the quotient is \( \Large x^{2}+ax+3 \) and remainder is \( \Large -3 +2b \). What are the values of a and b respectively?


A) 1, 0

B) 0,1

C) 1, 1

D) -1, -1

Correct Answer:
A) 1, 0

Description for Correct answer:
\( \Large x^{3}+2x^{2}+4x+b = \left(x+1\right) \left(x^{2}+ax+3\right)-3+2b \)

= \( \Large x^{3}+ \left(a+1\right)x^{2}+ \left(3+a\right)x+2b \)

Equating \( \Large a+1 = 2 \)

and \( \Large 2b = b \)

=> a = 1

and \( \Large b \left(2-1\right) = 0 \)

=> a = 1

and b = 0

Part of solved Polynomials questions and answers : >> Elementary Mathematics >> Polynomials




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