Question

Let c be a constant. When f (x) = 8xcube+cxsquare-5x+6 is divided by 2x+1, the remainder is 9. Find the value of c.

Answer 1

f(x) = 8x³ + cx² - 5x + 6

f(-1/2) = 8(-1/2)³ + c(-1/2)² - 5(-1/2) + 6 = 9

8(-1/8) + (1/4)c + (5/2) + 6 = 9

-1 + (1/4)c + (5/2) + 6 = 9

(1/4)c + (15/2) = 9

(1/4)c = 3/2

c = 6