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If ((x – 3)) is a factor of (2x^{3} + 3x^{2} – 17x – 30),…

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))