Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (w+2)(w+6) \)
Solution
Factor the expression \( w^2+8w+12 \).
Factor the expression by following steps:
- step0: Factor:
\(w^{2}+8w+12\)
- step1: Rewrite the expression:
\(w^{2}+6w+2w+12\)
- step2: Factor the expression:
\(w\left(w+6\right)+2\left(w+6\right)\)
- step3: Factor the expression:
\(\left(w+2\right)\left(w+6\right)\)
The fully factorized form of \( w^{2}+8w+12 \) is \((w+2)(w+6)\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To fully factorise \( w^{2}+8 w+12 \), we need to look for two numbers that multiply to \( 12 \) (the constant term) and add up to \( 8 \) (the coefficient of the \( w \) term). The numbers \( 6 \) and \( 2 \) fit this requirement, as \( 6 \times 2 = 12 \) and \( 6 + 2 = 8 \). Thus, we can express the quadratic as: \[ w^{2} + 8w + 12 = (w + 6)(w + 2) \] This is the fully factored form of the expression.
