Question

m² + 14m + 45

Explanation:

Step1: Find two numbers

Find two numbers that multiply to \(45\) and add to \(14\). The numbers are \(9\) and \(5\) since \(9\times5 = 45\) and \(9 + 5=14\).

Step2: Split the middle term

Rewrite the middle term \(14m\) as \(9m+5m\), so the expression becomes \(m^{2}+9m + 5m+45\).

Step3: Group and factor

Group the first two terms and the last two terms: \((m^{2}+9m)+(5m + 45)\). Factor out the GCF from each group: \(m(m + 9)+5(m + 9)\). Then factor out \((m + 9)\) to get \((m + 9)(m + 5)\).

Answer:

\((m + 9)(m + 5)\)