Polynomials

the cubic polynomial 2x^3-5x^2+ax+b is denoted by f(x). It is given that (x-2) is a factor of f(x),and that when f(x) is divided by (x-1) the remainder is -6. find the values of a and b.

the cubic polynomial 2x^3-5x^2+ax+b is denoted by f(x). It is given that (x-2) is a factor of f(x),and that when f(x) is divided by (x-1) the remainder is -6. find the values of a and b.

Any ideas? Do you know the factor theorem?

In class doing the question is easy but once at home it is as though a part of my brain shuts off

Ok I'll start you off:

If (x-2) is a factor of f(x) then this means that f(2) must be equal to 0.

To find f(2), you need to substitute 2 into 2x^3-5x^2+ax+b. Then set this to 0.


If (x-1) divided gives a remainder of -6 it means that f(1) = -6.


Have a go at this now and post all your working if you get stuck - it doesn't matter if your working is wrong.