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Factor Theorem

Find the valu...

Question

Find the value of 'a', if (x-a) is a factor of $x^{3} - a x^{2} + x + 2.$

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Solution

Let f(x) = $x^{3}$ – a $x^{2}$ + x + 2
It is given that (x – a) is a factor of f(x).
Remainder = f(a) = 0
$a^{3}$ – $a^{3}$ + a + 2 = 0
a + 2 = 0
a = -2

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