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Factor Theorem

fx=2x3-5x2+ax...

Question

$f (x) = 2 x^{3} - 5 x^{2} + a x + a$
Given that $(x + 2)$ is a factor of $f (x)$ , find the value of the constant $a$ .

- 16

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- 36

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Solution

The correct option is C $- 36$
$f (x) = 2 x^{3} - 5 x^{2} + a x + a$

$f (- 2) = 2 (- 2)^{3} - 5 (- 2)^{2} + a (- 2) + a = 0$

$- 16 - 20 - 2 a + a = 0$

$- a - 36 = 0$

$a = - 36$

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If $2$ and $0$ are the zeroes of the polynomial $f (x) = 2 x^{3} - 5 x^{2} + a x + b$ then find the values of $a$ and $b$ .

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f (x) = 2 x^{3} - 3 x^{2} - 17 x + 30

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