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