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

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

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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4k^2 + 7k + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $4k^2 + 7k + 3$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 4$
$b = 7$
$b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $4*3=12$ ) and add up to $b$ (which is $7$ ). $\newline$ The two numbers that satisfy these conditions are $4$ and $3$ because: $\newline$ $4 * 3 = 12$ $\newline$ $4 + 3 = 7$
Rewrite middle term: Rewrite the middle term, $7k$ , using the two numbers found in the previous step. $\newline$ $4k^2 + 7k + 3$ can be expressed as $4k^2 + 4k + 3k + 3$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(4k^2 + 4k) + (3k + 3)$
Factor out common factor: Factor out the common factor from each group. $\newline$ $4k(k + 1) + 3(k + 1)$
Factor out common factor: Since both groups contain the common factor $(k + 1)$ , factor this out. $(4k + 3)(k + 1)$