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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 − 4x^2 + x + 6, g(x) = x − 3 - 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 − 4x2 + x + 6, g(x) = x − 3

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Solution

If g(x) = x − 3 is a factor of the given polynomial p(x), then p(3) must be 0.

p(x) = x3 − 4 x2 + x + 6

p(3) = (3)3 − 4(3)2 + 3 + 6

       = 27 − 36 + 9

       = 0

Hence, g(x) = x − 3 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 2.3 | Page 44
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