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Factor. $\newline$ $n^2 + 7n + 10$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

n^2 + 7n + 10

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $n^2 + 7n + 10$ . $\newline$ The quadratic expression is in the standard form $ax^2 + bx + c$ , where $a = 1$ , $b = 7$ , and $b$ $0$ .
Find two numbers: Find two numbers that multiply to $a*c$ (which is $10$ ) and add up to $b$ (which is $7$ ). $\newline$ We need to find two numbers that multiply to $10$ and add up to $7$ . The numbers $2$ and $5$ satisfy these conditions because $2 \times 5 = 10$ and $2 + 5 = 7$ .
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(n + 2)(n + 5)$ , because these two binomials multiply to give the original quadratic expression.

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