Question

Find the remainder of the division of

x3 - 5x2 - 4x + 7 by x-7.

Select the appropriate response:

A) 99
B) 67
C) 77

Answer 1

C) 77

Explanation:

Using remainder theorem:

x = 7

7³ - 5(7)² - 4(7) + 7

77

Answer 2

Answer: C) 77

Remainder theorem: If p(x) is divided by (x-k), then the remainder is p(k)

In our case, p(x) = x^3-5x^2-4x+7 and k = 7

p(x) = x^3-5x^2-4x+7

p(7) = (7)^3-5(7)^2-4(7)+7

p(7) = 77

The remainder is 77

Side note: The nonzero remainder means x-7 is not a factor of x^3-5x^2-4x+7.

You can also use polynomial long division (see figure 1) or synthetic division (see figure 2). The figures are attached in the image below.