Find the value of a for which (x + 1) is a factor of $(a x^{3} + x^{2} - 2 x + 4 a - 9)$ .

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Solution

ANSWER:
Let $f (x) = a x^{3} + x^{2} - 2 x + 4 a - 9$
It is given that (x + 1) is a factor of f(x).
Using factor theorem, we have
f(−1) = 0
⇒ $a \times (- 1)^{3} + (- 1)^{2} - 2 \times - 1 + 4 a - 9 = 0 \Rightarrow - a + 1 + 2 + 4 a - 9 = 0 \Rightarrow 3 a - 6 = 0 \Rightarrow 3 a = 6 \Rightarrow a = 2$
Thus, the value of a is 2.

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