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Polynomials — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSPolynomials1 Mark
MCQ
Write the correct answer in the following$: x + 1$ is a factor of the polynomial.
  • ✓
    $x^3 + x^2 - x + 1$
  • B
    $x^3 + x^2 + x + 1$
  • C
    $x^4 + x^3 + x^2 + 1$
  • D
    $-x^4 + 3x^3 + 3x^2+ x + 1$
✓

Answer

Correct option: A.
$x^3 + x^2 - x + 1$
Let assume $(x + 1)$ is a factor of $x^3 + x^2 + x + 1$
So$, x = -1$ is zero of $x^3 + x^2 + x + 1$
$(-1)^3 + (-1)^2 + (-1) + 1 = 0$
$\Rightarrow -1 + 1 - 1 + 1 = 0$
$\Rightarrow 0 = 0$
Hence, our assumption is true.

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