Question

Find the value of a, such that (x-5) is a factor of x^3 - 3x^2 + ax - 10.

Answer 1

x³-ax²-13x+b has two factors. 
x-1 and x+3
x-1=0
x=1
and 
x+3=0
x= -3

Put x=1,
(1)³-a(1)²-13(1)+b=0
1-a-13+b=0
-a+b-12=0
-a+b=12----------------(1)

Put x=-3,
(-3)³-a(-3)²-13(-3)+b=0
-27-a(9)+36+b=0
-27-9a+36+b=0
-9a+b+12=0
-9a+b=-12----------------(2)

(1)-(2)
-a+b-(-9a+b)=12-(-12)
-a+b+9a-b=24
8a=24
a=24/8=3

-a+b=12
-3+b=12
b=12+3
b=15

So, a=3,b=15