Question

If x^2-x-6 and x^2+3x-18 have a common factor x-a then find the value of a?

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!!

Answer 2

p(x) = x2 - x - 6

f(x) = x2+3x-18 they have a common factor x-a

so when they are divided by x - a leave zero as they remainder By remainder theroem

p(a) = 0

f(a)=0

so p (a) = f(a)

a2 - 2-a - 6=a2 + 3a - 18

a2 - a2 - a - 3a = -18 + 6

-4a=-12

a=3. //-

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