Question

If ax^2-x-6 and x^2+3x-18 have a comman factor (x-a) then find the value of a.
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Answer 1

P(x)=x^2-x-6
f(x)=x^2+3x-18They have a common factor x-a 
So when they are divided by x-a leave zero as the remainder
By remainder theorem
p(a)=0
f(a)=0
So p(a)=f(a)
a^2-a-6=a^2+3a-18
a^2-a^2-a-3a= -18+6
-4a=-12
a=3

Hope it helps!!