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Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:- p(x) = 2x^3 + x^2 – 2x – 1, g(x) = x + 1 - Mathematics

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Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

p(x) = 2x3 + x2 – 2x – 1, g(x) = x + 1

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Solution

If g(x) = x + 1 is a factor of the given polynomial p(x), then p(−1) must be zero.

p(x) = 2x3 + x2 − 2x − 1

p(−1) = 2(−1)3 + (−1)2 − 2(−1) − 1

         = 2(−1) + 1 + 2 − 1

         = 0

Hence, g(x) = x + 1 is a factor of the given polynomial.

Concept: Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 9 Maths
Chapter 2 Polynomials
Exercise 2.4 | Q 2.1 | Page 44
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