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Factor. $\newline$ $q^2 + 3q + 2$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

q^2 + 3q + 2

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $q^2 + 3q + 2$ . Here, the coefficient of $q^2$ $(a)$ is $1$ , the coefficient of $q$ $(b)$ is $3$ , and the constant term $(c)$ is $2$ .
Find Multiplying Numbers: Find two numbers that multiply to the constant term $c$ and add up to the coefficient of $q$ $b$ . We need two numbers that multiply to $2$ $c$ and add up to $3$ $b$ . The numbers $1$ and $2$ satisfy these conditions because $1 \times 2 = 2$ and $q$ $0$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression $q^2 + 3q + 2$ is $(q + 1)(q + 2)$ .

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