Question

If the polynomial 4x3- 16x2 +ax +7 is exactly divisible by x-1, then find the value of a, hence factorise the polynomial.

Answer 1

as x - 1 is a factor
then p(1) must be 0.
so p(1) = 4 - 16 +a + 7 = 0
-12 +7 +a = 0
-5 + a = 0
a = 5