Find the HCF of f(x) = 6x^3 + 24x^2 + 18x, g(x) = 4x^4 + 4x^3 - 24x^2

Answer 1

I will assume that HCF means highest common factor. First factor them both and see what you get.
f(x) = 6x^3 + 24x^2 + 18x
= 6x(x^2 +4x +3)
= 6x(x+3)(x+1)
g(x) = 4x^4 + 4x^3 - 24x^2
= 4x^2(x^2 +x -6)
= 4x^2(x+3)(x-2)
2x(x+3) is the largest factor of both functions.
It goes into f(x) 3(x+1) times and
it goes into g(x) 2x(x-2) times