Question

factor completely.
2j^{2} + 9j + 7

Explanation:

Step1: Identify coefficients and constant

For quadratic \(2j^2 + 9j + 7\), \(a = 2\), \(b = 9\), \(c = 7\).

Step2: Find two numbers

Find two numbers that multiply to \(a\times c=2\times7 = 14\) and add to \(b = 9\). The numbers are \(2\) and \(7\) (since \(2 + 7=9\) and \(2\times7 = 14\)).

Step3: Split the middle term

Rewrite \(9j\) as \(2j+7j\):
\(2j^2+2j + 7j+7\)

Step4: Group and factor

Group the first two and last two terms:
\((2j^2 + 2j)+(7j + 7)\)
Factor out common factors from each group:
\(2j(j + 1)+7(j + 1)\)

Step5: Factor out \((j + 1)\)

Factor out \((j + 1)\) from both terms:
\((2j + 7)(j + 1)\)

Answer:

\((2j + 7)(j + 1)\)