Question

When x3+ cx + 4 is divided by (x + 2), the remainder is 4. Find the value of c.

Answer 1

Answer:

-4

Step-by-step explanation:

x³ + cx + 4 divided by x + 2 has a remainder of 4, so:

(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)

Multiply both sides by x + 2:

x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4

Distribute:

x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4

x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4

x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4

Match the coefficients.

a = 1

2a + b = 0

2b + d = c

2d + 4 = 4

Solving, a = 1, b = -2, and d = 0.  So c = -4.

We can also solve this using long division (see picture).