# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#3

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**Question**

The polynomial is given by

.

where b and c are integers.

**a. **Given that is a factor of show that .

**b. **The remainder when is divided by is -30.

Obtain a further equation in b and c.

**c. **Use equations from parts (a) and (b) to find the value of b and the value of c.

**Solution**

**a.
**

Factor theorem states that if is a factor of then;

For the given case is factor of .

We can write the divisor in standard form as;

Here and . Hence;

**b.
**

Remainder theorem states that if is divided by then;

For the given case is divided by and remainder is 65.

Here and . Hence;

**c. **

We are required to find values of b and c from equations obtained in parts (a) and (b).

These equations are;

Adding both equations;

Substituting in any of the equations obtained in parts (a) and (b).

We choose;

Hence;

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