# 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)?

##### 1 Answer

Jan 10, 2016

We know that **Remainder Theorem**

#### Explanation:

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

**Remainder**