Factor. 2f^2 + 13f + 11 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2f^2 + 13f + 11 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 13, c = 11.Find two numbers: Find two numbers that multiply to a*c (which is 2*11 = 22) and add up to b (which is 13). The numbers that satisfy these conditions are 2 and 11 because 2*11 = 22 and 2+11 = 13.Rewrite middle term: Rewrite the middle term 13f using the two numbers found in the previous step. The expression becomes 2f^2 + 2f + 11f + 11.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. This gives us (2f^2 + 2f) + (11f + 11).Factor out common factor: Factor out the greatest common factor from each group. From the first group, factor out 2f, which gives us 2f(f + 1). From the second group, factor out 11, which gives us 11(f + 1).Factor out final form: Since both groups contain the factor (f + 1), factor this out to get the final factored form. The factored form is (2f + 11)(f + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2f^2 + 13f + 11

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2f^2 + 13f + 11$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 13$ , $c = 11$ .
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*11 = 22$ ) and add up to $b$ (which is $13$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $11$ because $2*11 = 22$ and $2+11 = 13$ .
Rewrite middle term: Rewrite the middle term $13f$ using the two numbers found in the previous step. $\newline$ The expression becomes $2f^2 + 2f + 11f + 11$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ This gives us $(2f^2 + 2f) + (11f + 11)$ .
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $2f$ , which gives us $2f(f + 1)$ . $\newline$ From the second group, factor out $11$ , which gives us $11(f + 1)$ .
Factor out final form: Since both groups contain the factor $(f + 1)$ , factor this out to get the final factored form. The factored form is $(2f + 11)(f + 1)$ .