Question

find the value of a for which x + a is a factor of the polynomial F (x) = x^3 + ax^2 - 2x + a + 6​

Answer 1

Answer:

Hope it helps;

As, x -a is a factor of f(x), using factor theorem  f(-a) = 0;

f(-a) = (-a)^3 + a(-a)^2 - 2a + a + 6

0 =  -a^3 + a^3 -a + 6            {  a(-a)^2 becomes a^3 because -a^2 = a}

0 = -a + 6     ( a^3 and -a^3 cancels out )

-6 = -a

a  = 6