Question

2. 6x + nx - 14x + 2 is divisible by 2x + 1. The remainder is - 2. Find the value of n. Justify your answer by showing your work.

Answer 1

To find the value of n, we can use the factor theorem which states that if a polynomial f(x) is divisible by x - a, then f(a) = 0.

Given expression: 6x + nx - 14x + 2

Combine like terms:
6x - 14x + nx + 2 = -8x + nx + 2

Now we know that this expression is divisible by 2x + 1 with a remainder of -2. This means that:
-8(-2) + n(-2) + 2 = -2

16 - 2n + 2 = -2
18 - 2n = -2
-2n = -20
n = 10

Therefore, the value of n is 10.