Question

or the trinomial: $2x^2 + 19x + 42$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times42 = 84\) and add up to \(19\). The numbers are \(12\) and \(7\) since \(12\times7 = 84\) and \(12 + 7=19\).

Step2: Rewrite the middle term

Rewrite \(19x\) as \(12x+7x\) in the trinomial: \(2x^{2}+12x + 7x+42\).

Step3: Group and factor

Group the first two terms and the last two terms: \((2x^{2}+12x)+(7x + 42)\). Factor out the greatest common factor from each group: \(2x(x + 6)+7(x + 6)\).

Step4: Factor out the common binomial

Factor out the common binomial \((x + 6)\): \((2x + 7)(x + 6)\).

Answer:

\((2x + 7)(x + 6)\)