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\(5j^{2}-8j-4\) factors to \((j-2)(5j+2)\).
Solución
Factor the expression \( 5j^{2}-8j-4 \).
Factor the expression by following steps:
- step0: Factor:
\(5j^{2}-8j-4\)
- step1: Rewrite the expression:
\(5j^{2}+\left(2-10\right)j-4\)
- step2: Calculate:
\(5j^{2}+2j-10j-4\)
- step3: Rewrite the expression:
\(j\times 5j+j\times 2-2\times 5j-2\times 2\)
- step4: Factor the expression:
\(j\left(5j+2\right)-2\left(5j+2\right)\)
- step5: Factor the expression:
\(\left(j-2\right)\left(5j+2\right)\)
The factored form of \(5j^{2}-8j-4\) is \((j-2)(5j+2)\).
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Simplifique esta solución Extra Insights
To factor the quadratic expression \( 5j^{2}-8j-4 \), we look for two numbers that multiply to \( 5 \cdot (-4) = -20 \) and add up to \( -8 \). The numbers \( -10 \) and \( 2 \) fit the bill! We can rewrite the middle term: \[ 5j^2 - 10j + 2j - 4 \] Now, group the terms: \[ (5j^2 - 10j) + (2j - 4) \] Factor out the common terms: \[ 5j(j - 2) + 2(j - 2) \] This gives us: \[ (5j + 2)(j - 2) \] So, the complete factorization of \( 5j^{2}-8j-4 \) is: \[ (5j + 2)(j - 2) \] And voila! You've got your fully factored expression ready for action.
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