Question

FIND THE VALUE OF a IF x-a IS A FACTOR OF x^{​​​​​​3} - ax^{​​​​​2} - 2x + a-1

Answer 1

Let p(x) = x3 − ax2 + 2x + a − 1
Since (x − a) is a factor of p(x),
then p(a) = 0
⇒ (a)3 − a(a)2 + 2a + a − 1 = 0
⇒ a3 − a3 + 3a − 1 = 0
⇒ 3a − 1 = 0
⇒ 3a = 1⇒ a =1 /3