If $(x + 5)$ is a factor $(2 x^{3} + 9 x^{2} - 11 x + a)$ . Find $30 - a$ .

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Solution

$(x + 5)$ is a factor of $2 x^{3} + 9 x^{2} - 11 x + a$
Factor theorem says, that $x = - 5$ will be a root of the given polynomial.
So, $2 {(- 5)}^{3} + 9 {(- 5)}^{2} - 11 (- 5) + a = 0$
$\Rightarrow 2 (- 125) + 9 (25) + 55 + a = 0$
$\Rightarrow - 250 + 225 + 55 + a = 0$
$\Rightarrow a = - 30.$
Hence, the answer is $- 30.$

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Similar questions

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 2 x^{3} + 9 x^{2} - 11 x - 30, g (x) = x + 5$

69 + 11 x - x^{2} + x^{3}

x + 2 x^{3} - 9 x^{2} + 12

Question 16
Show that:
(i) x + 3 is a factor of $69 + 11 x - x^{2} + x^{3}$ .

(ii) 2x – 3 is a factor of $x + 2 x^{3} - 9 x^{2} + 12$ .

Question 16
Show that:
(i) x + 3 is a factor of $69 + 11 x - x^{2} + x^{3}$ .

(ii) 2x – 3 is a factor of $x + 2 x^{3} - 9 x^{2} + 12$ .

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