Factor. n^2 + 5n + 6 ____

Identify Coefficients: Identify the coefficients for n^2, n, and the constant term. The quadratic expression is n^2 + 5n + 6. Here, the coefficient of n^2 (a) is 1, the coefficient of n (b) is 5, and the constant term (c) is 6.Find Multiplying Numbers: Determine two numbers that multiply to give the constant term (c) and add up to the coefficient of n (b). We need to find two numbers that multiply to 6 and add up to 5. The numbers 2 and 3 satisfy these conditions because 2 * 3 = 6 and 2 + 3 = 5.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression n^2 + 5n + 6 is (n + 2)(n + 3).

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

\newline

n^2 + 5n + 6

Identify Coefficients: Identify the coefficients for $n^2$ , $n$ , and the constant term. $\newline$ The quadratic expression is $n^2 + 5n + 6$ . Here, the coefficient of $n^2$ ( $a$ ) is $1$ , the coefficient of $n$ ( $b$ ) is $5$ , and the constant term ( $c$ ) is $n$ $0$ .
Find Multiplying Numbers: Determine two numbers that multiply to give the constant term $c$ and add up to the coefficient of $n$ ( $b$ ). $\newline$ We need to find two numbers that multiply to $6$ and add up to $5$ . The numbers $2$ and $3$ satisfy these conditions because $2 \times 3 = 6$ and $2 + 3 = 5$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression $n^2 + 5n + 6$ is $(n + 2)(n + 3)$ .