Factor. 2w^2 + 5w + 3 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2w^2 + 5w + 3 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 5, c = 3Find numbers and sum: Find two numbers that multiply to a*c (which is 2*3 = 6) and add up to b (which is 5). The numbers that satisfy these conditions are 2 and 3 because 2*3 = 6 and 2+3 = 5.Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in the previous step. 2w^2 + 5w + 3 can be rewritten as 2w^2 + 2w + 3w + 3.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2w^2 + 2w) + (3w + 3)Factor out common factor: Factor out the greatest common factor from each group. 2w(w + 1) + 3(w + 1)Final factorization: Since both groups contain the common factor (w + 1), factor this out. (2w + 3)(w + 1)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2w^2 + 5w + 3

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2w^2 + 5w + 3$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 5$ , $c = 3$
Find numbers and sum: Find two numbers that multiply to $a*c$ (which is $2*3 = 6$ ) and add up to $b$ (which is $5$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $3$ because $2*3 = 6$ and $2+3 = 5$ .
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in the previous step. $\newline$ $2w^2 + 5w + 3$ can be rewritten as $2w^2 + 2w + 3w + 3$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2w^2 + 2w) + (3w + 3)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $2w(w + 1) + 3(w + 1)$
Final factorization: Since both groups contain the common factor $(w + 1)$ , factor this out. $(2w + 3)(w + 1)$