Factor. 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 ax^2 + bx + c. a = 2, b = 13, c = 11Find suitable 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 2 and 11 because 2*11 = 22 and 2+11 = 13.Rewrite middle term: Rewrite the middle term 13t using the two numbers found in Step 2. 2t^2 + 13t + 11 can be rewritten as 2t^2 + 2t + 11t + 11.Factor by grouping: Factor by grouping. Group the terms into two pairs and factor out the common factor from each pair. From the first pair (2t^2 + 2t), factor out 2t to get 2t(t + 1). From the second pair (11t + 11), factor out 11 to get 11(t + 1).Write factored form: Write the factored form by combining the common factors. Since both groups contain the factor (t + 1), the factored form is (2t + 11)(t + 1).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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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 $ax^2 + bx + c$ . $a = 2$ , $b = 13$ , $c = 11$
Find suitable 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 $2$ and $11$ because $2*11 = 22$ and $2+11 = 13$ .
Rewrite middle term: Rewrite the middle term $13t$ using the two numbers found in Step $2$ . $\newline$ $2t^2 + 13t + 11$ can be rewritten as $2t^2 + 2t + 11t + 11$ .
Factor by grouping: Factor by grouping. Group the terms into two pairs and factor out the common factor from each pair. $\newline$ From the first pair $2t^2 + 2t$ , factor out $2t$ to get $2t(t + 1)$ . $\newline$ From the second pair $11t + 11$ , factor out $11$ to get $11(t + 1)$ .
Write factored form: Write the factored form by combining the common factors. $\newline$ Since both groups contain the factor $(t + 1)$ , the factored form is $(2t + 11)(t + 1)$ .