# What is the remainder when (2x^{3} + 4x^{2} - 32x + 18) ÷ (x - 3)?

**Solution:**

Given, (2x^{3} + 4x^{2} - 32x + 18) ÷ (x - 3)

We have to find the remainder.

By long division,

Therefore, the remainder is 12.

**Alternate method -**

The remainder theorem is stated as follows: When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).

Using the remainder theorem

x = 3

Substituting it we get

f(3) = 2(3)^{3} + 4(3)^{2} - 32(3) + 18

f(3) = 2(27) + 4 (9) - 32 (3) + 18

So we get

f(3) = 54 + 36 - 96 + 18

f(3) = 12

Therefore, the remainder is 12.

## What is the remainder when (2x^{3} + 4x^{2} - 32x + 18) ÷ (x - 3)?

**Summary:**

The remainder when (2x^{3} + 4x^{2} - 32x + 18) ÷ (x - 3) is 12.

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