In Example 3, change the x + 4 to x + 3 and then find the remainder.

Data from Example 3

By using the remainder theorem, determine the remainder when 3x³ − x² − 20x + 5 is divided by x + 4.

In using the remainder theorem, we determine the remainder when the function is divided by x − r by evaluating the function for x = r. To have x + 4 in the proper form to identify r, we write it as x − (−4). This means that r = −4, and we therefore evaluate the function f(x) = 3x³ − x² − 20x + 5 for x = −4, or find f(−4):

The remainder is −123 when 3x³ − x² − 20x + 5 is divided by x + 4.

(-4)= 3(-4) - (-4) - 20(-4) + 5 = 192 - 16 + 80 + 5 - 123 =