Question

question
factor the trinomial:
$5x^2 + 34x + 24$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times24 = 120\) and add up to \(34\). The numbers are \(30\) and \(4\) since \(30\times4 = 120\) and \(30 + 4=34\).

Step2: Rewrite the middle term

Rewrite \(34x\) as \(30x+4x\) in the trinomial: \(5x^{2}+30x + 4x+24\).

Step3: Group and factor

Group the first two terms and the last two terms: \((5x^{2}+30x)+(4x + 24)\). Factor out the greatest common factor from each group: \(5x(x + 6)+4(x + 6)\).

Step4: Factor out the common binomial

Factor out \((x + 6)\) from both terms: \((5x + 4)(x + 6)\).

Answer:

\((5x + 4)(x + 6)\)