Question

(iii) (x - 2) is a factor of x3 + 2x2 + ax - 6. Also
verify if (x + 3) is also a factor.

Answer 1

Answer:

a = -5

Step-by-step explanation:

If x-2 is a factor of the given function then by factor theorem we have when x=2,

$f(2)=0$

$2^{3}+2*2^{2}+2*a-6=0$

8+8+2a-6 = 0

2a = -10

a = -5

If x+3 be a factor, then by factor theorem

$f(-3)=0$

$(-3)^{3}+2(-3^{2})-5(-3)-6=0$

-27 + 18 + 15 - 6 = 0

0 = 0

Which is true fundamentally

Hence,  (x+3) is a factor of f(x)