Question

Find the value of a. if (x + 2) is a factor of the
polynomial f(x) = x^3 + 13x^2 + ax + 20
(a) -15
(b) 20
(c) 25
(d) 32​

Answer 1

$\huge\boxed{Answer}$

Given :-

(x + 2) is a factor of the polynomial

f(x) = x³ + 13x² + ax + 20

So , x + 2 = 0

x = -2

Then , f(-2) = 0

(-2)³ + 13(-2)² + a(-2) + 20 = 0

-8 + 13(4) - 2a + 20 = 0

-8 + 52 - 2a + 20 = 0

-2a + 64 = 0

2a = 64

a = 32