Factor. n^2 + 8n + 15 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression n^2 + 8n + 15. The quadratic expression is in the form of an^2 + bn + c, where a = 1, b = 8, and c = 15.Find two numbers: Find two numbers that multiply to c (15) and add up to b (8). We need to find two numbers that when multiplied give us 15 and when added give us 8. The numbers 3 and 5 satisfy these conditions because 3 * 5 = 15 and 3 + 5 = 8.Write factored form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (n + 3)(n + 5), because these two binomials multiply to give the original quadratic expression n^2 + 8n + 15.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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n^2 + 8n + 15

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $n^2 + 8n + 15$ . $\newline$ The quadratic expression is in the form of $an^2 + bn + c$ , where $a = 1$ , $b = 8$ , and $b$ $0$ .
Find two numbers: Find two numbers that multiply to $c$ ( $15$ ) and add up to $b$ ( $8$ ). $\newline$ We need to find two numbers that when multiplied give us $15$ and when added give us $8$ . The numbers $3$ and $5$ satisfy these conditions because $3 \times 5 = 15$ and $3 + 5 = 8$ .
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(n + 3)(n + 5)$ , because these two binomials multiply to give the original quadratic expression $n^2 + 8n + 15$ .