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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 3y^2 + 7y + 4 by comparing it to 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 7y using the two numbers found in the previous step. 3y^2 + 7y + 4 can be rewritten as 3y^2 + 3y + 4y + 4.Group and factor: Group the terms into two pairs and factor by grouping. Group (3y^2 + 3y) and (4y + 4). Factor out the greatest common factor from each group. From (3y^2 + 3y), factor out 3y: 3y(y + 1). From (4y + 4), factor out 4: 4(y + 1).Notice common factor: Notice that both groups now contain the common factor (y + 1). Write the expression as the product of (y + 1) and the other factors. The factored form is (3y + 4)(y + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3y^2 + 7y + 4

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $3y^2 + 7y + 4$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 3$ $b = 7$ $c = 4$
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: $\newline$ $3 \times 4 = 12$ $\newline$ $3 + 4 = 7$
Rewrite middle term: Rewrite the middle term $7y$ using the two numbers found in the previous step. $3y^2 + 7y + 4$ can be rewritten as $3y^2 + 3y + 4y + 4$ .
Group and factor: Group the terms into two pairs and factor by grouping. $\newline$ Group $(3y^2 + 3y)$ and $(4y + 4)$ . $\newline$ Factor out the greatest common factor from each group. $\newline$ From $(3y^2 + 3y)$ , factor out $3y$ : $3y(y + 1)$ . $\newline$ From $(4y + 4)$ , factor out $4$ : $4(y + 1)$ .
Notice common factor: Notice that both groups now contain the common factor $(y + 1)$ . $\newline$ Write the expression as the product of $(y + 1)$ and the other factors. $\newline$ The factored form is $(3y + 4)(y + 1)$ .