Question

question
factor the trinomial:
$3x^2 + 10x + 8$

Explanation:

Step1: Find pair for ac=24, sum=10

We need two numbers that multiply to $3\times8=24$ and add to $10$. These numbers are 6 and 4.

Step2: Split middle term

Rewrite $10x$ as $6x+4x$:
$3x^2 + 6x + 4x + 8$

Step3: Factor by grouping

Group first/last two terms, factor GCF:
$3x(x+2) + 4(x+2)$

Step4: Factor out common binomial

Extract $(x+2)$ from both terms:
$(3x+4)(x+2)$

Answer:

$(3x+4)(x+2)$