Question

factor.
$5x^2 + 12x + 7$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times7 = 35\) and add up to \(12\). The numbers are \(5\) and \(7\) since \(5\times7=35\) and \(5 + 7=12\).

Step2: Rewrite the middle term

Rewrite \(12x\) as \(5x+7x\) in the expression \(5x^{2}+12x + 7\), so we get \(5x^{2}+5x+7x + 7\).

Step3: Group and factor

Group the first two terms and the last two terms: \((5x^{2}+5x)+(7x + 7)\). Factor out the common factors from each group: \(5x(x + 1)+7(x + 1)\). Then factor out \((x + 1)\) to get \((5x + 7)(x+1)\).

Answer:

\((5x + 7)(x + 1)\)