Question

factor the trinomial: $5x^2 + 31x + 6$

Explanation:

Step1: Identify coefficients

For $5x^2 + 31x + 6$, $a=5$, $b=31$, $c=6$

Step2: Find product $a \times c$

$a \times c = 5 \times 6 = 30$

Step3: Find pair summing to $b$

Find two numbers that multiply to 30 and add to 31: 30 and 1

Step4: Split middle term

$5x^2 + 30x + x + 6$

Step5: Factor by grouping

$5x(x + 6) + 1(x + 6)$

Step6: Factor out common binomial

$(5x + 1)(x + 6)$

Answer:

$(5x + 1)(x + 6)$