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Mathematical Statements

One of the fa...

Question

One of the factors of $x^{3} + 3 x^{2} - x - 3$ is :

x + 1

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x - 1

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x + 3

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x - 3

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Solution

The correct options are
A $x - 1$
B $x + 3$
C $x + 1$
Solving this question by looking at options,
$f (1) = 1 + 3 - 1 - 3 = 0$
$f (- 1) = - 1 + 3 + 1 - 3 = 0$
$f (- 3) = - 27 + 27 + 3 - 3 = 0$
$f (3) = 27 + 27 - 3 - 3$ $\neq$ $0$
$∴$ $x - 1, x + 1, x + 3$ are factors but $x - 3$ is not a factor.

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