Question
Step 2: In each grouping, factor out the common factor. \[ \left(5 w^{2}+2 w\right)+(-15 w-6)=w(\square)-3(\square) \]
Ask by Hodges Nguyen. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression \(5w^2+2w-15w-6\) can be factored as \(w(5w+2)-3(5w+2)\).
Solution
Factor the expression \( 5w^2+2w-15w-6 \).
Factor the expression by following steps:
- step0: Factor:
\(5w^{2}+2w-15w-6\)
- step1: Factor the expression:
\(w\left(5w+2\right)-3\left(5w+2\right)\)
- step2: Factor the expression:
\(\left(w-3\right)\left(5w+2\right)\)
The factored form of the expression \(5w^2+2w-15w-6\) is \((w-3)(5w+2)\).
Therefore, the expression can be rewritten as \(w(5w+2)-3(5w+2)\).
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Simplify this solution Beyond the Answer
To factor out the common factor in the expression \((5w^2 + 2w) + (-15w - 6)\), first, simplify within the parentheses: 1. Combine: \(5w^2 + 2w - 15w - 6\) simplifies to \(5w^2 - 13w - 6\). Now, let's identify and factor out the common factors: - For \(5w^2 + 2w\), the common factor is \(w\), so it becomes \(w(5w + 2)\). - For \(-15w - 6\), the common factor is \(-3\), so it becomes \(-3(5w + 2)\). Thus, we have: \[ w(5w + 2) - 3(5w + 2) \] Now, we can factor out the common binomial \((5w + 2)\): \[ (w - 3)(5w + 2) \]
