Factor. u^2 + 13u + 22 ____

Identify Coefficients: Identify the coefficients for u^2, u, and the constant term. The quadratic expression is u^2 + 13u + 22. Here, the coefficient of u^2 (a) is 1, the coefficient of u (b) is 13, and the constant term (c) is 22.Find Multiplying Numbers: Find two numbers that multiply to give the constant term (c = 22) and add up to the coefficient of u (b = 13). We need to find two numbers m and n such that m * n = 22 and m + n = 13.List Factors and Sum: List the factors of 22 and determine which pair adds up to 13. The factors of 22 are 1 and 22, 2 and 11. The pair that adds up to 13 is 2 and 11 because 2 + 11 = 13.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (u + 2)(u + 11) because these two binomials multiply to give the original quadratic expression.

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

\newline

u^2 + 13u + 22

Identify Coefficients: Identify the coefficients for $u^2$ , $u$ , and the constant term. $\newline$ The quadratic expression is $u^2 + 13u + 22$ . Here, the coefficient of $u^2$ ( $a$ ) is $1$ , the coefficient of $u$ ( $b$ ) is $13$ , and the constant term ( $c$ ) is $u$ $0$ .
Find Multiplying Numbers: Find two numbers that multiply to give the constant term $c = 22$ and add up to the coefficient of $u$ $b = 13$ . We need to find two numbers $m$ and $n$ such that $m \times n = 22$ and $m + n = 13$ .
List Factors and Sum: List the factors of $22$ and determine which pair adds up to $13$ . The factors of $22$ are $1$ and $22$ , $2$ and $11$ . The pair that adds up to $13$ is $2$ and $11$ because $13$ $0$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression is $(u + 2)(u + 11)$ because these two binomials multiply to give the original quadratic expression.