Factor. 2t^(2)+13 t+11

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2t^2 + 13t + 11 by comparing it to the standard form at^2 + bt + c. a = 2 b = 13 c = 11Find two numbers: Find two numbers that multiply to a*c (which is 2*11 = 22) and add up to b (which is 13). The two numbers that satisfy these conditions are 11 and 2 because: 11 * 2 = 22 11 + 2 = 13Rewrite middle term: Write the middle term (13t) as the sum of two terms using the numbers found in the previous step. 2t^2 + 13t + 11 can be rewritten as: 2t^2 + 11t + 2t + 11Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2t^2 + 11t) + (2t + 11)Factor out common factor: Factor out the greatest common factor from each group. t(2t + 11) + 1(2t + 11)Final factorization: Since both groups contain the common factor (2t + 11), factor this out. (2t + 11)(t + 1)

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Q. Factor.

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2t^{2}+13t+11

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2t^2 + 13t + 11$ by comparing it to the standard form $at^2 + bt + c$ . $a = 2$ $b = 13$ $c = 11$
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 two numbers that satisfy these conditions are $11$ and $2$ because: $\newline$ $11 \times 2 = 22$ $\newline$ $11 + 2 = 13$
Rewrite middle term: Write the middle term $13t$ as the sum of two terms using the numbers found in the previous step. $2t^2 + 13t + 11$ can be rewritten as: $2t^2 + 11t + 2t + 11$
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2t^2 + 11t) + (2t + 11)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $t(2t + 11) + 1(2t + 11)$
Final factorization: Since both groups contain the common factor $(2t + 11)$ , factor this out. $(2t + 11)(t + 1)$