Question

question
factor the trinomial:
$2x^2 + 19x + 42$

Explanation:

Step1: Identify \(a\), \(b\), \(c\)

For \(2x^{2}+19x + 42\), \(a = 2\), \(b = 19\), \(c = 42\).

Step2: Find \(ac\)

Calculate \(ac=2\times42 = 84\).

Step3: Find factors of \(84\)

Find two numbers that multiply to \(84\) and add to \(19\). The numbers are \(12\) and \(7\) (\(12\times7 = 84\), \(12 + 7=19\)).

Step4: Split the middle term

Rewrite the middle term: \(2x^{2}+12x + 7x+42\).

Step5: Group and factor

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

Answer:

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