If ((x – 3)) is a factor of (2x^{3} + 3x^{2} – 17x – 30), find the remaining factors.
-
A.
(2x – 5)(x – 2) -
B.
(2x – 5)(x + 2) -
C.
(2x + 5)(x – 2) -
D.
(2x + 5)(x + 2)
Correct Answer: Option D
Explanation
Divide (2x^{3} + 3x^{2} – 17x – 30) by ((x – 3)). You get (2x^{2} + 9x + 10).
Factorizing, we have (2x^{2} + 9x + 10 = 2x^{2} + 4x + 5x + 10)
(2x(x + 2) + 5(x + 2))
= ((2x + 5)(x + 2))