Factor. y^2 + 9y + 14 ____

Identify Variables: Identify a, b, and c in the quadratic expression y^2 + 9y + 14. Compare y^2 + 9y + 14 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 9, and c = 14.Find Multiplying Numbers: Find two numbers that multiply to ac (which is just c since a = 1) and add up to b. We need two numbers that multiply to 14 and add up to 9. The numbers 2 and 7 satisfy these conditions because: 2 * 7 = 14 (product is c) 2 + 7 = 9 (sum is b)Rewrite Expression: Write the quadratic expression using the two numbers found in Step 2. The expression y^2 + 9y + 14 can be rewritten as y^2 + 2y + 7y + 14.Factor by Grouping: Factor by grouping. Group the terms to factor by common terms: (y^2 + 2y) + (7y + 14) Factor out the common factors from each group: y(y + 2) + 7(y + 2)Factor Common Binomial: Factor out the common binomial factor. Since both groups contain the factor (y + 2), we can factor it out: (y + 2)(y + 7)

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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y^2 + 9y + 14

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $y^2 + 9y + 14$ . Compare $y^2 + 9y + 14$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 9$ , and $c = 14$ .
Find Multiplying Numbers: Find two numbers that multiply to $ac$ (which is just $c$ since $a = 1$ ) and add up to $b$ . We need two numbers that multiply to $14$ and add up to $9$ . The numbers $2$ and $7$ satisfy these conditions because: $2 \times 7 = 14$ (product is $c$ ) $c$ $0$ (sum is $b$ )
Rewrite Expression: Write the quadratic expression using the two numbers found in Step $2$ . $\newline$ The expression $y^2 + 9y + 14$ can be rewritten as $y^2 + 2y + 7y + 14$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor by common terms: $\newline$ $(y^2 + 2y) + (7y + 14)$ $\newline$ Factor out the common factors from each group: $\newline$ $y(y + 2) + 7(y + 2)$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the factor $(y + 2)$ , we can factor it out: $\newline$ $(y + 2)(y + 7)$