Factor. 5y^2 + 8y + 3 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 5y^2 + 8y + 3. Compare 5y^2 + 8y + 3 with the standard form ax^2 + bx + c. a = 5 b = 8 c = 3Find numbers for multiplication: Find two numbers that multiply to a*c (which is 5*3=15) and add up to b (which is 8). We need to find two numbers that multiply to 15 and add up to 8. The numbers 3 and 5 satisfy these conditions because 3*5 = 15 and 3+5 = 8.Rewrite middle term: Rewrite the middle term 8y using the two numbers found in Step 2. We can express 8y as 3y + 5y. So, 5y^2 + 8y + 3 can be rewritten as 5y^2 + 3y + 5y + 3.Group and factor terms: Group the terms into two pairs and factor each pair. We have 5y^2 + 3y and 5y + 3. Factor out the greatest common factor from each pair. From 5y^2 + 3y, we can factor out y to get y(5y + 3). From 5y + 3, we can factor out 1 (since there is no common factor other than 1) to get 1(5y + 3).Factor by grouping: Factor by grouping. We now have y(5y + 3) + 1(5y + 3). Since 5y + 3 is common to both terms, we can factor it out. The factored form is (5y + 3)(y + 1).

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Factor. $\newline$ $5y^2 + 8y + 3$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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5y^2 + 8y + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5y^2 + 8y + 3$ . Compare $5y^2 + 8y + 3$ with the standard form $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find numbers for multiplication: Find two numbers that multiply to $a*c$ (which is $5*3=15$ ) and add up to $b$ (which is $8$ ). $\newline$ We need to find two numbers that multiply to $15$ and add up to $8$ . $\newline$ The numbers $3$ and $5$ satisfy these conditions because $3*5 = 15$ and $3+5 = 8$ .
Rewrite middle term: Rewrite the middle term $8y$ using the two numbers found in Step $2$ . $\newline$ We can express $8y$ as $3y + 5y$ . $\newline$ So, $5y^2 + 8y + 3$ can be rewritten as $5y^2 + 3y + 5y + 3$ .
Group and factor terms: Group the terms into two pairs and factor each pair. $\newline$ We have $5y^2 + 3y$ and $5y + 3$ . $\newline$ Factor out the greatest common factor from each pair. $\newline$ From $5y^2 + 3y$ , we can factor out $y$ to get $y(5y + 3)$ . $\newline$ From $5y + 3$ , we can factor out $1$ (since there is no common factor other than $1$ ) to get $1(5y + 3)$ .
Factor by grouping: Factor by grouping. $\newline$ We now have $y(5y + 3) + 1(5y + 3)$ . $\newline$ Since $5y + 3$ is common to both terms, we can factor it out. $\newline$ The factored form is $(5y + 3)(y + 1)$ .