Question

Consider the polynomial function P(x) = 2x^3 - mx^2 + x - 5m. The remainder when P(x) is divided

by (x - 2) is four times the remainder from dividing P(x) by (x + 1). Determine m algebraically
and show all your work.​

Answer 1

m = 57/14 =
`4(1)/(14)`

Explanation:

The polynomial can be expressed as follows;

P(x) = 2·x³ - m·x² + x - 5·m

(2·x³ - m·x² + x - 5·m) ÷ (x - 2)

2·x²

(-m - 2)·x² + x

(-m - 2)·x

(m + 3)·x - 5·m

(m + 3)·x

-5·m

The remainder = -5·m/(x -2)

Similarly, dividing by (x + 1) will give a remainder of -5·m/(x + 1)

But -5·m/(x -2) = 4×-5·m/(x + 1)

5/(x -2) = 20/(x + 1)

5(x + 1) = 20(x -2)

20x - 5x= 40 + 5

x = 45/15 = 3

2·3³ - m·3² + 3 - 5·m = 54 - 9m + 3 - 5m = 57 - 14m

(57 - 14m)/1 = (57 - 14m)/4

228 - 56m =57 - 14m

171 = 56m-14m = 42m

m = 171/42 = 57/14.