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Factor. Check by multiplying. \( 5 x^{2}+40 x \) \( 5 x^{2}+40 x=\square \)

Ask by Ruiz Welch. in the United States
Feb 24,2025

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\(5x(x + 8)\)

Solución

Factor the expression \( 5x^2+40x \). Factor the expression by following steps: - step0: Factor: \(5x^{2}+40x\) - step1: Rewrite the expression: \(5x\times x+5x\times 8\) - step2: Factor the expression: \(5x\left(x+8\right)\) The factored form of the expression \(5x^2+40x\) is \(5x(x+8)\). Now, let's check by multiplying: \(5x(x+8) = 5x^2 + 40x\) Multiplying the terms, we get: \(5x^2 + 40x = 5x^2 + 40x\) Therefore, the factored form \(5x(x+8)\) is equivalent to the original expression \(5x^2+40x\).

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The Deep Dive

You can factor out the greatest common factor from the expression \(5x^2 + 40x\). The greatest common factor here is \(5x\), so you can rewrite the expression as \(5x(x + 8)\). To check your work, simply multiply \(5x\) by \((x + 8)\): \(5x \cdot x + 5x \cdot 8 = 5x^2 + 40x\), which means your factorization is correct! Now you have \(5x(x + 8)\) as the factored form of your original expression. Remember, factoring is just like unwrapping a present — you’re revealing what’s inside!

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