Question

factor the trinomial:
$3x^2 + 25x + 42$

Explanation:

Step1: Multiply leading & constant terms

$3 \times 42 = 126$

Step2: Find pair summing to 25

We need two numbers that multiply to 126 and add to 25: $18$ and $7$ (since $18 \times 7 = 126$, $18 + 7 = 25$)

Step3: Split middle term

$3x^2 + 18x + 7x + 42$

Step4: Factor by grouping

$$\begin{align} &3x(x + 6) + 7(x + 6) \\ &=(3x + 7)(x + 6) \end{align}$$

Answer:

$(3x + 7)(x + 6)$