Factor. 3x^2 + 8x + 4 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3x^2 + 8x + 4. Compare 3x^2 + 8x + 4 with the standard form ax^2 + bx + c. a = 3 b = 8 c = 4Find Factors and Sum: Find two numbers that multiply to a*c (which is 3*4=12) and add up to b (which is 8). We need to find two numbers that satisfy these conditions. After checking possible pairs of factors of 12, we find that 2 and 6 are the numbers we are looking for because 2*6 = 12 and 2 + 6 = 8.Rewrite Middle Term: Rewrite the middle term 8x using the two numbers 2 and 6 found in Step 2. 3x^2 + 8x + 4 can be written as 3x^2 + 2x + 6x + 4.Factor by Grouping: Factor by grouping. Group the terms into two pairs: (3x^2 + 2x) and (6x + 4). Factor out the greatest common factor from each pair. From 3x^2 + 2x, we can factor out x to get x(3x + 2). From 6x + 4, we can factor out 2 to get 2(3x + 2).Write Factored Form: Write the factored form of the expression. We have x(3x + 2) and 2(3x + 2). Both groups have a common factor of (3x + 2). Factor out (3x + 2) to get the final factored form: (x + 2)(3x + 2).

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Factor. $\newline$ $3x^2 + 8x + 4$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3x^2 + 8x + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3x^2 + 8x + 4$ . Compare $3x^2 + 8x + 4$ with the standard form $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find Factors and Sum: Find two numbers that multiply to $a*c$ (which is $3*4=12$ ) and add up to $b$ (which is $8$ ). $\newline$ We need to find two numbers that satisfy these conditions. $\newline$ After checking possible pairs of factors of $12$ , we find that $2$ and $6$ are the numbers we are looking for because $2*6 = 12$ and $2 + 6 = 8$ .
Rewrite Middle Term: Rewrite the middle term $8x$ using the two numbers $2$ and $6$ found in Step $2$ . $\newline$ $3x^2 + 8x + 4$ can be written as $3x^2 + 2x + 6x + 4$ .
Factor by Grouping: Factor by grouping. Group the terms into two pairs: $(3x^2 + 2x)$ and $(6x + 4)$ . Factor out the greatest common factor from each pair. From $3x^2 + 2x$ , we can factor out $x$ to get $x(3x + 2)$ . From $6x + 4$ , we can factor out $2$ to get $2(3x + 2)$ .
Write Factored Form: Write the factored form of the expression. $\newline$ We have $x(3x + 2)$ and $2(3x + 2)$ . Both groups have a common factor of $(3x + 2)$ . $\newline$ Factor out $(3x + 2)$ to get the final factored form: $(x + 2)(3x + 2)$ .