Question
Factor out the greatest common factor. \[ -6 z^{2}+12 z \]
Ask by Hammond Barrett. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Factor out \(-6z\) to get \(-6z(z-2)\).
Solution
Factor the expression \( -6z^{2}+12z \).
Factor the expression by following steps:
- step0: Factor:
\(-6z^{2}+12z\)
- step1: Factor the expression:
\(-6\left(z^{2}-2z\right)\)
- step2: Factor the expression:
\(-6z\left(z-2\right)\)
The greatest common factor of the expression \(-6z^{2}+12z\) is \(-6z\). Factoring out the greatest common factor, we get \(-6z(z-2)\).
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Simplify this solution Beyond the Answer
To factor out the greatest common factor (GCF) from the expression \( -6 z^{2}+12 z \), we first identify the GCF of the coefficients and the variable parts. The GCF of \(-6\) and \(12\) is \(6\). Additionally, both terms contain at least one \(z\), so \(z\) is also part of the GCF. Thus, the GCF is \(6z\). Now we factor it out: \[ -6z^{2} + 12z = 6z(-z + 2) \] So, the factored form is: \[ 6z(-z + 2) \]
