# Using the remainder theorem, how do you find the remainder of #3x^5-5x^2+4x+1# when it is divided by #(x-1)(x+2)#?

##### 1 Answer

#### Explanation:

Let us denote, by

**polynomial (poly.).**

Noting that the **divisor poly.,** i.e., **degree**

**degree** of the **remainder (poly.)** sought for, must be

**less than**

Therefore, we suppose that, the **remainder** is

Now, if **quotient poly.,** then, by the **Remainder Theorem,**

we have,

We prefer,

Sub.ing,

Similarly, sub.inf

Solving

These give us the **desired remainder,**

**Enjoy Maths.!**