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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2k^2 + 13k + 11 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 13, c = 11.Find suitable numbers: Find two numbers that multiply to a*c (2*11 = 22) and add up to b (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 13k using the two numbers found in the previous step. 2k^2 + 13k + 11 can be rewritten as 2k^2 + 2k + 11k + 11.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2k^2 + 2k) + (11k + 11).Factor out common factor: Factor out the greatest common factor from each group. 2k(k + 1) + 11(k + 1).Final factored form: Since both groups contain the common factor (k + 1), factor this out. The factored form is (2k + 11)(k + 1).

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2k^2 + 13k + 11

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2k^2 + 13k + 11$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 13$ , $c = 11$ .
Find suitable numbers: Find two numbers that multiply to $a*c$ ( $2*11 = 22$ ) and add up to $b$ ( $13$ ). $\newline$ 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 $13k$ using the two numbers found in the previous step. $\newline$ $2k^2 + 13k + 11$ can be rewritten as $2k^2 + 2k + 11k + 11$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2k^2 + 2k) + (11k + 11)$ .
Factor out common factor: Factor out the greatest common factor from each group. $2k(k + 1) + 11(k + 1)$ .
Final factored form: Since both groups contain the common factor $(k + 1)$ , factor this out. $\newline$ The factored form is $(2k + 11)(k + 1)$ .