Factorize completely {x³ + 3x² - 10x}{2x² - 8}

Correct Answer is : x(x+5)2(x+2)

Correct Answer is : x(x+5)2(x+2)

Test Index

JAMB Mathematics 2010 Paper

Question : 5

Total: 49

\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}

Solution:

Concept:

Simplify the rational expression by factoring both the numerator and denominator, then cancel common factors.

Explanation:

Factor the numerator by taking out the common factor

x

x^{3} + 3x^{2} - 10x = x(x^{2} + 3x - 10)

Factor the quadratic

x^{2} + 3x - 10

x^{2} + 3x - 10 = (x - 2)(x + 5)

Factor the denominator:

2x^{2} - 8 = 2(x^{2} - 4) = 2(x - 2)(x + 2)

Write the full factored form:

\frac{x(x - 2)(x + 5)}{2(x - 2)(x + 2)}

Cancel the common factor

(x - 2)

\frac{x(x + 5)}{2(x + 2)}

Answer:

\frac{x(x + 5)}{2(x + 2)}

This corresponds to option C.

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