Q. 12 A4.9( 7 Votes )

Let us calculate and write the value of a for which x + a will be a factor of the polynomial x3 + ax2 – 2x + a – 12.

We have the polynomial as x3 + ax2 – 2x + a – 12.

Given that x + a is the factor of the polynomial, which means that x = -a is the root of the polynomial.

So f(-a) = 0.

(-a)3 + a(-a)2 - 2(-a) + a – 12 = 0

-a3 + a3 + 2a + a – 12 = 0

3a – 12 = 0

3a = 12

a = 4.

value of a is 4.

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