Question

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

Explanation:

Step1: Split middle term

Find two numbers that multiply to $5\times12=60$ and add to 23. These numbers are 20 and 3.
$5x^2 + 20x + 3x + 12$

Step2: Group terms

Pair the first two and last two terms.
$(5x^2 + 20x) + (3x + 12)$

Step3: Factor out GCFs

Factor greatest common factors from each group.
$5x(x + 4) + 3(x + 4)$

Step4: Factor common binomial

Extract the shared binomial factor.
$(5x + 3)(x + 4)$

Answer:

$(5x + 3)(x + 4)$