The expression x3 – 4×2 + 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: Option C
Explanation
F(X) = x3 – 4×2 + 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