Which factor is true of the trinomial: $10 x^{2} + 3 x - 1$ ?

2 x^{2} + 5 x - 1

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(2 x + 1) (5 x - 1)

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(2 x + 1)^{2} (5 x - 1)

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(2 x + 1)^{2}

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Solution

The correct option is B $(2 x + 1) (5 x - 1)$
$10 x^{2} + 3 x - 1$
$= 10 x^{2} + 5 x - 2 x - 1$ (Rewrite $3 x$ as $5 x - 2 x$ to make grouping and factoring easier.)
$= 5 x (2 x + 1) - 1 (2 x + 1)$
$= (2 x + 1) (5 x - 1)$
Therefore $10 x^{2} + 3 x - 1 = (2 x + 1) (5 x - 1)$

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