Factor. 2u^2 + 7u + 5 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2u^2 + 7u + 5 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 7, c = 5Find suitable numbers: Find two numbers that multiply to a*c (2*5 = 10) and add up to b (7). The numbers that satisfy these conditions are 2 and 5, since 2*5 = 10 and 2+5 = 7.Rewrite middle term: Rewrite the middle term, 7u, using the two numbers found in the previous step. 2u^2 + 7u + 5 can be rewritten as 2u^2 + 2u + 5u + 5.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2u^2 + 2u) + (5u + 5)Factor out common factor: Factor out the greatest common factor from each group. 2u(u + 1) + 5(u + 1)Final factorization: Since both groups contain the common factor (u + 1), factor this out. (2u + 5)(u + 1)

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2u^2 + 7u + 5

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2u^2 + 7u + 5$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 7$ , $c = 5$
Find suitable numbers: Find two numbers that multiply to $a*c$ ( $2*5 = 10$ ) and add up to $b$ ( $7$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $5$ , since $2*5 = 10$ and $2+5 = 7$ .
Rewrite middle term: Rewrite the middle term, $7u$ , using the two numbers found in the previous step. $\newline$ $2u^2 + 7u + 5$ can be rewritten as $2u^2 + 2u + 5u + 5$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2u^2 + 2u) + (5u + 5)$
Factor out common factor: Factor out the greatest common factor from each group. $2u(u + 1) + 5(u + 1)$
Final factorization: Since both groups contain the common factor $(u + 1)$ , factor this out. $(2u + 5)(u + 1)$