Question

For what value of a will x + 2 be a factor of 2x3 + 4x2 − ax + 12?

Answer 1

Answer:

f(x) =

$2 {x}^{3} + 4 {x}^{2} - ax + 12$

$x + 2 = 0 \\ x = - 2$

f(-2) =

$2( { - 2}^{3}) + 4( { - 2}^{2}) - a( - 2) + 12 \\ 2( - 8) + 4(4) + 2a + 12 \\ - 16 + 16 + 2a + 12 \\ 2a + 12 = 0 \\ 2a = - 12 \\ a = \frac{ - 12}{2 } \\ a = - 6$