Factor. y^2 + 5y + 4 ____

Identify Variables: Identify a, b, and c in the quadratic expression y^2 + 5y + 4. The quadratic expression is in the form y^2 + by + c, where a = 1, b = 5, and c = 4.Find Two Numbers: Find two numbers that multiply to c (4) and add up to b (5). We are looking for two numbers that when multiplied give us 4 and when added give us 5. The numbers 1 and 4 satisfy these conditions because 1 * 4 = 4 and 1 + 4 = 5.Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (y + 1)(y + 4), because these two binomials multiply to give the original quadratic expression y^2 + 5y + 4.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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y^2 + 5y + 4

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $y^2 + 5y + 4$ . The quadratic expression is in the form $y^2 + by + c$ , where $a = 1$ , $b = 5$ , and $c = 4$ .
Find Two Numbers: Find two numbers that multiply to $c$ ( $4$ ) and add up to $b$ ( $5$ ). $\newline$ We are looking for two numbers that when multiplied give us $4$ and when added give us $5$ . The numbers $1$ and $4$ satisfy these conditions because $1 \times 4 = 4$ and $1 + 4 = 5$ .
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(y + 1)(y + 4)$ , because these two binomials multiply to give the original quadratic expression $y^2 + 5y + 4$ .