Use the reminder theorem to factorize the following expression : ${2 x}^{3} + x^{2} - 13 x + 6.$

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Solution

Let
$f (x) = 2 x 3 + x 2 - 13 x + 6$
Now, Factors of constant term $6$ are $\pm 1, \pm 2, \pm 3, \pm 6$ .
Putting $x = 2$ , we have
$f (2) = 2 (2) 3 + 22 - 13 (2) + 6 = 16 + 4 - 26 + 6 = 0$
$∴$ By factor theorem, $(x - 2)$ is a factor of $f (x)$

Now we divide $f (x)$ by $(x - 2)$ to get the other factor by long divison method as shown.
therefore : $2 x^{3} + x^{2} - 13 x + 6$ = $(x - 2) \times (2 x^{2} + 5 x - 3)$ +0

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Use the reminder theorem to factorize the following expression : 2x3+x2−13x+6.

Use the reminder theorem to factorize the following expression : ${2 x}^{3} + x^{2} - 13 x + 6.$