Question

factor completely. 2m² + 12m - 32

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(2m^{2}\), \(12m\), and \(-32\) is \(2\). So we factor out \(2\) from the polynomial:
\(2m^{2}+12m - 32=2(m^{2}+6m - 16)\)

Step2: Factor the quadratic

Now we need to factor the quadratic \(m^{2}+6m - 16\). We look for two numbers that multiply to \(- 16\) and add up to \(6\). The numbers are \(8\) and \(-2\) because \(8\times(-2)=-16\) and \(8+( - 2)=6\). So we can factor \(m^{2}+6m - 16\) as \((m + 8)(m-2)\)

Step3: Combine the factors

Putting it all together, the completely factored form of the original polynomial is \(2(m + 8)(m - 2)\)

Answer:

\(2(m + 8)(m - 2)\)