Question

question
factor the trinomial:
$5x^2 + 23x + 12$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times12 = 60\) and add up to \(23\). The numbers are \(20\) and \(3\) since \(20\times3=60\) and \(20 + 3=23\).

Step2: Rewrite the middle term

Rewrite the trinomial \(5x^{2}+23x + 12\) as \(5x^{2}+20x+3x + 12\).

Step3: Group and factor

Group the first two terms and the last two terms: \((5x^{2}+20x)+(3x + 12)\).
Factor out the greatest common factor from each group: \(5x(x + 4)+3(x + 4)\).

Step4: Factor out the common binomial

Now factor out the common binomial \((x + 4)\): \((5x + 3)(x + 4)\).

Answer:

\((5x + 3)(x + 4)\)