If $(x - 3)$ and $(x - 2)$ are two factors of the polynomial $x^{3} - 6 x^{2} + 11 x - 6$ , find the third factor.

x - 1

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x - 4

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x - 5

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x - 6

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Solution

The correct option is A $x - 1$
$(x - 3) (x - 2) = x^{2} - 5 x + 6$
Now, for finding the third factor, divide the polynomial with $(x^{2} - 5 x + 6)$

$\begin{matrix} x - 1 x^{2} - 5 x + 6 x^{3} - 6 x^{2} + 11 x - 6 x^{3} - 5 x^{2} + 6 x - ------------- - - x^{2} + 5 x - 6 - x^{2} + 5 x - 6 - ------------- - 0 \end{matrix}$
So, $(x - 1)$ is the third factor.

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Similar questions

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x).

f(x) = $x^{3} - 6 x^{2}$ + 11x - 6; g(x) = x - 3

If (x - 3) and (x - 2) are two factors of the polynomial x^{3} - 6 x^{2} + 11 x - 6, then find the third factor.

f (x) = x^{3} - 6 x^{2} + 11 x - 6

x^{3} + 6 x^{2} + 11 x + 6

(x + 1)

(x + 1) (x + 2) (x + 3)

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