Problem: If two factors of 2x3−hx+k2 x^{3}-h x+k2x3−hx+k are x+2x+2x+2 and x−1x-1x−1, the value of ∣2h−3k∣|2 h-3 k|∣2h−3k∣ is
Answer Choices:
A. 444
B. 333
C. 222
D. 111
E. 000 Solution:
Write f(x)=2x3−hx+kf(x)=2 x^{3}-h x+kf(x)=2x3−hx+k. Then f(−2)=−16+2h+k=0f(-2)=-16+2 h+k=0f(−2)=−16+2h+k=0 and f(1)=2−h+k=0f(1)=2-h+k=0f(1)=2−h+k=0. Hence h=6,k=4h=6, k=4h=6,k=4 and ∣2h−3k∣=0|2 h-3 k|=0∣2h−3k∣=0.