Question

find the value of a if x-a is a factor of x cube -a x square +2x+a-1

Answer 1

Let p(x)=x^3-ax^2+2x+a-1
According to factor theorem if x-a is factor of

p(a)=0
So,
p(a)=a^3-a(a)^2+2a+a-1
p(a)=a^3-3^3+3a-1
p(a)=3a-1

Now,
3a-1=0
3a=1
a=1/3 Ans.

Answer 2

Let p(x)=x^3-ax^2+2x+a-1
Let g(x)=x-a=0
x=a
As g(x) is a factor of p(x)
By factor theorem
Remainder=0
P(a)=a^3-a(a)^2+2(a)+a-1=0
a^3-a^3+2a+a-1=0
3a-1=0
3a=1
a=1/3