Factor. 3u^2 + 22u + 7 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3u^2 + 22u + 7 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 22 c = 7Find numbers for ac: Find two numbers that multiply to a*c (3*7=21) and add up to b (22). We need to find two numbers that satisfy these conditions.Use numbers in expression: After trying different combinations, we find that the numbers 1 and 21 multiply to 21 and add up to 22. 1 * 21 = 21 1 + 21 = 22Rewrite middle term: Rewrite the middle term 22u using the two numbers found in the previous step. 3u^2 + 22u + 7 can be rewritten as 3u^2 + 1u + 21u + 7.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (3u^2 + 1u) + (21u + 7)Factor out common factor: Factor out the greatest common factor from each group. u(3u + 1) + 7(3u + 1)Since both groups contain the common factor (3u + 1), factor this out. (u + 7)(3u + 1)

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Factor. $\newline$ $3u^2 + 22u + 7$

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

\newline

3u^2 + 22u + 7

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3u^2 + 22u + 7$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 3$
$b = 22$
$b$ $0$
Find numbers for $ac$ : Find two numbers that multiply to $a*c$ ( $3\times7=21$ ) and add up to $b$ ( $22$ ). $\newline$ We need to find two numbers that satisfy these conditions.
Use numbers in expression: After trying different combinations, we find that the numbers $1$ and $21$ multiply to $21$ and add up to $22$ . $\newline$ $1 \times 21 = 21$ $\newline$ $1 + 21 = 22$
Rewrite middle term: Rewrite the middle term $22u$ using the two numbers found in the previous step. $\newline$ $3u^2 + 22u + 7$ can be rewritten as $3u^2 + 1u + 21u + 7$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(3u^2 + 1u) + (21u + 7)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $u(3u + 1) + 7(3u + 1)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $u(3u + 1) + 7(3u + 1)$ Since both groups contain the common factor $(3u + 1)$ , factor this out. $\newline$ $(u + 7)(3u + 1)$