To factor the quadratic equation \(7x^2 = 56x\), we first rewrite it in standard form:
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Put the quadratic in standard form: \[ 7x^2 - 56x = 0 \]
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Factor out the GCF: The greatest common factor of \(7x^2\) and \(-56x\) is \(7x\): \[ 7x(x - 8) = 0 \]
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Set each factor equal to zero:
- \(7x = 0\) gives \(x = 0\)
- \(x - 8 = 0\) gives \(x = 8\)
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The solutions are: \[ x = 0 \quad \text{and} \quad x = 8 \]
Thus, the correct response is:
Put the quadratic in standard form \(7x^2 - 56x = 0\)
Factor out the GCF \(7x(x - 8) = 0\)
Set each factor equal to zero \(7x = 0\) and \(x - 8 = 0\)
The solutions are \(x = 0\) and \(x = 8\)
This matches the second response option provided in your list.