Question

question
factor the trinomial:
$5x^2 + 31x + 30$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times30 = 150\) and add up to \(31\). The numbers are \(25\) and \(6\) since \(25\times6 = 150\) and \(25 + 6=31\).

Step2: Rewrite the middle term

Rewrite the trinomial as \(5x^{2}+25x + 6x+30\).

Step3: Group and factor

Group the first two terms and the last two terms: \((5x^{2}+25x)+(6x + 30)\). Factor out the greatest common factor from each group: \(5x(x + 5)+6(x + 5)\).

Step4: Factor out the common binomial

Factor out \((x + 5)\) to get \((5x + 6)(x + 5)\).

Answer:

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