Question

Find the polynomial function of degree 3 such that f(2)=24 and x-1, x and x+2 are factors of the polynomial

Answer 1

f(x) = 3x^3 + 3x^2 - 6x.

Explanation:

Let:

f(x) = x(x - 1)(x + 2)

= x(x^2 + x - 2)

= x^3 + x^2 - 2x - this might be the answer or it might be some multiple of this.

Now f(2) = 24 so

24 = a(2^3 + 2^2 - 2(2)) where a is a constant.

24 = 8a

a = 3

So the function is

3( x^3 + x^2 - 2x)

= 3x^3 + 3x^2 - 6x.