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Factor completely. \( -5 v^{2}-28 v-15 \) \( \square \square \square \)

Ask by Li Elliott. in the United States
Feb 24,2025

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Tutor-Verified Answer

Answer

The expression \( -5v^{2}-28v-15 \) factors to \( -(v+5)(5v+3) \).

Solution

Factor the expression \( -5v^2-28v-15 \). Factor the expression by following steps: - step0: Factor: \(-5v^{2}-28v-15\) - step1: Factor the expression: \(-\left(5v^{2}+28v+15\right)\) - step2: Factor the expression: \(-\left(v+5\right)\left(5v+3\right)\) The factored form of the expression \( -5v^{2}-28v-15 \) is \( -(v+5)(5v+3) \).

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The Deep Dive

To factor the expression \( -5v^{2} - 28v - 15 \) completely, first, we can factor out a negative sign to make it easier: \( - (5v^{2} + 28v + 15) \). Next, we look for two numbers that multiply to \( (5)(15) = 75 \) and add up to \( 28 \). These numbers are \( 25 \) and \( 3 \). Now we rewrite the middle term: \( 5v^{2} + 25v + 3v + 15 \). Group the terms: \( (5v^{2} + 25v) + (3v + 15) \). Factoring by grouping gives: \( 5v(v + 5) + 3(v + 5) \). Now we can factor out \( (v + 5) \): \( (v + 5)(5v + 3) \). Thus, the factored form is: \(- (v + 5)(5v + 3)\).

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