Question

factor completely.
$5t^{2}+12t + 4$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times4 = 20\) and add up to \(12\). The numbers are \(10\) and \(2\) since \(10\times2 = 20\) and \(10 + 2=12\).

Step2: Rewrite the middle term

Rewrite \(12t\) as \(10t+2t\) in the expression \(5t^{2}+12t + 4\), so we get \(5t^{2}+10t+2t + 4\).

Step3: Group the terms

Group the first two terms and the last two terms: \((5t^{2}+10t)+(2t + 4)\).

Step4: Factor out the GCF from each group

Factor out \(5t\) from the first group and \(2\) from the second group: \(5t(t + 2)+2(t + 2)\).

Step5: Factor out the common binomial factor

Factor out \((t + 2)\) from both terms: \((5t + 2)(t + 2)\).

Answer:

\((5t + 2)(t + 2)\)