# Find the remainder when f(x) = x^{3} - 14x^{2} + 51x - 22 is divided by x - 7?

**Solution:**

Given: f(x) = x^{3} - 14x^{2} + 51x - 22

We should divide it by x - 7

Using the remainder theorem, let us evaluate the remainder

f(x) = x^{3} - 14x^{2} + 51x - 22

f(7) = (7)^{3} - 14(7)^{2} + 51(7) - 22

By further calculation,

f(7) = 343 - 14(49) + 357 - 22

So we get,

f(7) = 343 - 686 + 357 - 22

f(7) = -8

Therefore, the remainder is -8.

## Find the remainder when f(x) = x^{3} - 14x^{2} + 51x - 22 is divided by x - 7?

**Summary:**

The remainder when f(x) = x^{3} - 14x^{2} + 51x - 22 is divided by x - 7 is -8.