What is the remainder of x3 + 3x2 − 10x + k divided by (x + 4)?

k + 24

Explanation:

1) I will use synthetic division

2) Write the coefficients of the dividend keeping the decreasing order of the exponents of x.

     1         3         - 10       + k

3) dividing by x + 4 => run the synthetic division with x = - 4

4) division

     | 1     3     -10     +k
     |
-4  |       -4    + 4      +24

      1     -1    - 6       k + 24

The last number is the remainder: k + 24

Sis less than or equal to 75 (bottom left)