Question
Factor completely. \( 5 g^{2}+24 g-5 \) \( \square \) Submit
Ask by Spencer Nunez. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(5g^{2}+24g-5\) factors to \((g+5)(5g-1)\).
Solution
Factor the expression \( 5g^2+24g-5 \).
Factor the expression by following steps:
- step0: Factor:
\(5g^{2}+24g-5\)
- step1: Rewrite the expression:
\(5g^{2}+\left(-1+25\right)g-5\)
- step2: Calculate:
\(5g^{2}-g+25g-5\)
- step3: Rewrite the expression:
\(g\times 5g-g+5\times 5g-5\)
- step4: Factor the expression:
\(g\left(5g-1\right)+5\left(5g-1\right)\)
- step5: Factor the expression:
\(\left(g+5\right)\left(5g-1\right)\)
The factored form of the expression \(5g^{2}+24g-5\) is \((g+5)(5g-1)\).
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Simplify this solution Mind Expander
To factor the quadratic expression \( 5g^{2} + 24g - 5 \), we look for two numbers that multiply to \( 5 \times -5 = -25 \) and add to \( 24 \). The numbers \( 25 \) and \( -1 \) fit the bill perfectly! We rewrite the expression as: \( 5g^{2} + 25g - g - 5 \). Next, we can group and factor by grouping: \( (5g^{2} + 25g) + (-g - 5) \) which gives us: \( 5g(g + 5) - 1(g + 5) \). Now, we factor out \( (g + 5) \): \( (g + 5)(5g - 1) \). So, the completely factored form of \( 5g^{2} + 24g - 5 \) is \( (g + 5)(5g - 1) \). Now you can dazzle your friends with your factoring prowess! 🌟
