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Factorisation Using Factor Theorem

Solve: 5x2 ...

Question

Solve: $(5 x^{2} + 10 x) \div (x + 2)$

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Solution

$(5 x^{2} + 10 x) \div (x + 2) = \frac{5 x^{2} + 10 x}{x + 2}$
Let us factorize the numerator $(5 x^{2} + 10 x)$
$5 x^{2} + 10 x = (5 \times x \times x) + (5 \times 2 \times x)$
$= 5 x (x + 2)$ [Taking out the common factor $5 x$ ]
Now, $(5 x^{2} + 10 x) \div (x + 2) = \frac{5 x^{2} + 10 x}{x + 2}$
$= \frac{5 x (x + 2)}{(x + 2)} = 5 x$ . [By cancelling $(x + 2)]$

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