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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) = x^3 + 3x^2 + 3x + 1, g(x) = x + 2 - 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) = x3 + 3x2 + 3x + 1, g(x) = x + 2

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Solution

If g(x) = x + 2 is a factor of the given polynomial p(x), then p(−2) must be 0.

p(x) = x3 +3x2 + 3x + 1

p(−2) = (−2)3 + 3(−2)2 + 3(−2) + 1

         = − 8 + 12 − 6 + 1

         = −1

As p(−2) ≠ 0,

Hence, g(x) = x + 2 is not 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 2.2 | Page 44
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