Question

factor completely. \\(2f^2 + 13f + 11\\)

Explanation:

Step1: Identify coefficients and constant

For quadratic \(2f^2 + 13f + 11\), \(a = 2\), \(b = 13\), \(c = 11\). We need two numbers that multiply to \(a\times c=2\times11 = 22\) and add to \(b = 13\). The numbers are \(11\) and \(2\) (since \(11\times2 = 22\) and \(11 + 2=13\)).

Step2: Split the middle term

Rewrite the middle term using these numbers: \(2f^2+2f + 11f+11\).

Step3: Group and factor

Group the first two and last two terms: \((2f^2 + 2f)+(11f + 11)\). Factor out common factors from each group: \(2f(f + 1)+11(f + 1)\).

Step4: Factor out the common binomial

Now, factor out \((f + 1)\) from both terms: \((2f + 11)(f + 1)\).

Answer:

\((2f + 11)(f + 1)\)