Find the remainder when f(x) = x³ - 14x² + 51x - 22 is divided by x - 7?

Solution:

Given: f(x) = x³ - 14x² + 51x - 22

We should divide it by x - 7

Using the remainder theorem, let us evaluate the remainder

f(x) = x³ - 14x² + 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) = x³ - 14x² + 51x - 22 is divided by x - 7?

Summary:

The remainder when f(x) = x³ - 14x² + 51x - 22 is divided by x - 7 is -8.