The expression x3 - 4x2 + cx + d is such that x + 1 is its factor, and its value is 1 when x is -2. Find c and d.
A. c = 4 and d = -9
B. c = -4 and d = 9
C. c = -20 and d = -15
D. c = 20 and d = -15
E. c = -20 and d = 15
Correct Answer: C
Explanation
F(X) = x3 - 4x2 + cx + d
= (X + 1) Q(X) + R
x = -1, R = 0,f(-1) = -13 - 4(-1)2 + c(-1) + d = 0
-1 - 4 - c + d = 0
d - c = 5................(i)
f(-2) = -23 - 4(-2)2 + c(-2) + d = 1
= -8 - 16 - 2c + d
= 1
-8 - 16 - 2c + d = 1
-24 - 2c + d = 1
d - 2c = 1 + 24
d - 2c = 25.................(ii)
\(\frac{d - c = 5}{-c = 20}\) d - c = 5
c = -20
d - (-20) = 5
d + 20 = 5
d = 5 - 20
= -15
c = -20, d = -15
