Question

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

Answer 1

Answer:

m = 57/14 = $4\frac{1}{14}$

Step-by-step 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.