Question

question
factor the trinomial:
$5x^2 + 22x + 8$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times8 = 40\) and add up to \(22\). The numbers are \(20\) and \(2\) since \(20\times2 = 40\) and \(20 + 2=22\).

Step2: Rewrite the middle term

Rewrite \(22x\) as \(20x+2x\) in the trinomial: \(5x^{2}+20x + 2x+8\).

Step3: Group and factor

Group the first two terms and the last two terms: \((5x^{2}+20x)+(2x + 8)\). Factor out the greatest common factor from each group: \(5x(x + 4)+2(x + 4)\).

Step4: Factor out the common binomial

Factor out the common binomial \((x + 4)\): \((5x + 2)(x + 4)\).

Answer:

\((5x + 2)(x + 4)\)