Question

The polynomial y = 2x3 + mx2

- 13x + n has a remainder of 0 when
divided by (x - 2) and (x - 3). Find the value of m + n:

Answer 1

2x³ + mx² - 13x + n

y = x - 2

x = 2

2(2)³ + m(2)² - 13(2) + n = 0

16 + 4m - 26 + n = 0

4m + n = 10. (1)

y = x - 3

x = 3

therefore 9m + n = -15

solving simultaneously

m = -5, n = 30

m + n = 25