-11
-9
-3
4
Correct answer is C
Using the remainder theorem, the remainder when a polynomial ax2+bx+c is divided by (x−a) is equal to f(a).
2x3+3x2+qx−1 divided by (x+2), the remainder = f(−2)
⟹f(−2)=f(1)
f(−2)=2(−23)+3(−22)+q(−2)−1=−16+12−2q−1=−5−2q
f(1)=2(13)+3(12)+q(1)−1=2+3+q−1=4+q
4+q=−5−2q⟹4+5=−2q−q=−3q
q=−3
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