Solve x^2 + 6x + 5 = 0.

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Solve x^2 + 6x + 5 = 0.

Explanation:
When solving a quadratic by factoring, we look for two numbers that multiply to the constant term (5) and add to the coefficient of x (6). Those numbers are 1 and 5, so the expression factors as (x + 1)(x + 5) = 0. A product is zero when either factor is zero, giving x + 1 = 0 or x + 5 = 0, so x = -1 or x = -5. You can verify by substitution: (-1)^2 + 6(-1) + 5 = 0 and (-5)^2 + 6(-5) + 5 = 0. The quadratic formula would also yield -1 and -5, confirming both solutions.

When solving a quadratic by factoring, we look for two numbers that multiply to the constant term (5) and add to the coefficient of x (6). Those numbers are 1 and 5, so the expression factors as (x + 1)(x + 5) = 0. A product is zero when either factor is zero, giving x + 1 = 0 or x + 5 = 0, so x = -1 or x = -5. You can verify by substitution: (-1)^2 + 6(-1) + 5 = 0 and (-5)^2 + 6(-5) + 5 = 0. The quadratic formula would also yield -1 and -5, confirming both solutions.

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