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

Identify Coefficients: Identify the coefficients a, b, and c in the quadratic expression 2v^2 + 13v + 11 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 13, c = 11Find Multiplying 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 of the quadratic expression using the two numbers found in Step 2. 2v^2 + 13v + 11 can be rewritten as 2v^2 + 2v + 11v + 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 (2v^2 + 2v), factor out 2v to get 2v(v + 1). From the second pair (11v + 11), factor out 11 to get 11(v + 1).Write Factored Form: Write the factored form of the expression by factoring out the common binomial (v + 1). The expression becomes (2v + 11)(v + 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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2v^2 + 13v + 11

Identify Coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2v^2 + 13v + 11$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 13$ , $c = 11$
Find Multiplying 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 of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2v^2 + 13v + 11$ can be rewritten as $2v^2 + 2v + 11v + 11$ .
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 $2v^2 + 2v$ , factor out $2v$ to get $2v(v + 1)$ . $\newline$ From the second pair $11v + 11$ , factor out $11$ to get $11(v + 1)$ .
Write Factored Form: Write the factored form of the expression by factoring out the common binomial $(v + 1)$ . The expression becomes $(2v + 11)(v + 1)$ .