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The expression x\(^3\) - 4x\(^2\) + cx + d is such that...

The expression x\(^3\) - 4x\(^2\) + 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 is C

F(X) = x\(^3\) - 4x\(^2\) + cx + d

= (X + 1) Q(X) + R

x = -1, R = 0,f(-1) = -1\(^3\) - 4(-1)\(^2\) + c(-1) + d = 0

-1 - 4 - c + d = 0

d - c = 5................(i)

f(-2) = -2\(^3\) - 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