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Determine If the Following Polynomial Has (X + 1) a Factor :- X3 + X2 + X + 1 - Mathematics

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Sum

Determine if the following polynomial has (x + 1) a factor :-

x3 + x2 + x + 1

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Solution

If (x + 1) is a factor of p(x) = x3 + x2 + x + 1, then p (−1) must be zero, otherwise (x + 1) is not a factor of p(x).

p(x) = x3 + x2 + x + 1

p(−1) = (−1)3 + (−1)2 + (−1) + 1

          = − 1 + 1 − 1 + 1

          = 0

Hence, x + 1 is a factor of this 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 1.1 | Page 43
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