Factor. 3u^2 + 7u + 4 ____

Identify Variables: Identify a, b, and c in the quadratic expression 3u^2 + 7u + 4 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 7 c = 4Find Two Numbers: Find two numbers that multiply to a*c (which is 3*4=12) and add up to b (which is 7). The two numbers that satisfy these conditions are 3 and 4 because: 3 * 4 = 12 3 + 4 = 7Rewrite Middle Term: Rewrite the middle term, 7u, using the two numbers found in the previous step. 3u^2 + 7u + 4 can be rewritten as 3u^2 + 3u + 4u + 4.Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. (3u^2 + 3u) + (4u + 4)Factor out Common Factor: Factor out the greatest common factor from each group. 3u(u + 1) + 4(u + 1)Final Factored Form: Since both groups contain the common factor (u + 1), factor this out. (3u + 4)(u + 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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3u^2 + 7u + 4

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $3u^2 + 7u + 4$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 7$ $\newline$ $c = 4$
Find Two Numbers: Find two numbers that multiply to $a*c$ (which is $3*4=12$ ) and add up to $b$ (which is $7$ ). $\newline$ The two numbers that satisfy these conditions are $3$ and $4$ because: $\newline$ $3 * 4 = 12$ $\newline$ $3 + 4 = 7$
Rewrite Middle Term: Rewrite the middle term, $7u$ , using the two numbers found in the previous step. $\newline$ $3u^2 + 7u + 4$ can be rewritten as $3u^2 + 3u + 4u + 4$ .
Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(3u^2 + 3u) + (4u + 4)$
Factor out Common Factor: Factor out the greatest common factor from each group. $3u(u + 1) + 4(u + 1)$
Final Factored Form: Since both groups contain the common factor $(u + 1)$ , factor this out. $(3u + 4)(u + 1)$