$(x - 3)$ is a factor of $(2 x^{3} + 7 x^{2} - 24 x - a)$ .Then find $a$

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Solution

Since $x - 3$ is a factor of the polynomial $2 x^{3} + 7 x^{2} - 24 x - a$ , therefore we substitute $x = 3$ in the given polynomial and equate it to $0$ to find the value of $a$ as shown below:

$2 x^{3} + 7 x^{2} - 24 x - a = 0 \Rightarrow 2 (3)^{3} + 7 (3)^{2} - (24 \times 3) - a = 0 \Rightarrow (2 \times 27) + (7 \times 9) - 72 - a = 0 \Rightarrow 54 + 63 - 72 - a = 0 \Rightarrow 54 + 63 - 72 - a = 0 \Rightarrow 45 - a = 0 \Rightarrow a = 45$

Hence, $a = 45$ .

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