When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2, how do you determine the remainder when the polynomial is divided by (x+2)(x-1)?
We know that
Now find the remainder of polynomial f(x) when divided by (x-1)(x+2)
The remainder will be of the form Ax + B, because it is the remainder after division by a quadratic.
We can now multiply the divisor times the quotient Q ...
Next, insert 1 and -2 for x ...
Solving these two equations, we get A = 7 and B = -5