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Determine Which of the Following Polynomials Has (X + 1) a Factor :- X4 + 3x3 + 3x2 + X + 1 - Mathematics

Sum

Determine which of the following polynomials has (x + 1) a factor :-

x4 + 3x3 + 3x2 + x + 1

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Solution

If (x + 1) is a factor of polynomial p(x) = x4 + 3x3 + 3x2 + x + 1, then p(−1) must be 0, otherwise (x + 1) is not a factor of this polynomial.

p(−1) = (−1)4 + 3(−1)3 + 3(−1)2 + (−1) + 1

          = 1 − 3 + 3 − 1 + 1

          = 1

As p(−1) ≠ 0,

Therefore, x + 1 is not a factor of this polynomial.

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APPEARS IN

NCERT Class 9 Mathematics Textbook
Chapter 2 Polynomials
Exercise 2.4 | Q 1.3 | Page 43
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