Question

factor the trinomial: $3x^2 + 23x + 30$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $3\times30=90$ and add to 23. The numbers are 18 and 5.
Rewrite the trinomial: $3x^2 + 18x + 5x + 30$

Step2: Group terms

Group the first two and last two terms: $(3x^2 + 18x) + (5x + 30)$

Step3: Factor out GCFs

Factor GCF from each group: $3x(x + 6) + 5(x + 6)$

Step4: Factor common binomial

Factor out $(x+6)$ from both terms: $(3x + 5)(x + 6)$

Answer:

$(3x + 5)(x + 6)$