Factor. v^2 + 9v + 20 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is v^2 + 9v + 20. Here, the coefficient of v^2 (a) is 1, the coefficient of v (b) is 9, and the constant term (c) is 20.Find Multiplying Numbers: Find two numbers that multiply to the constant term (c) and add up to the coefficient of v (b). We need to find two numbers that multiply to 20 and add up to 9. The numbers 4 and 5 satisfy these conditions because 4 * 5 = 20 and 4 + 5 = 9.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (v + 4)(v + 5), because when we expand this, we get v^2 + 4v + 5v + 20, which simplifies to v^2 + 9v + 20.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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v^2 + 9v + 20

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $v^2 + 9v + 20$ . Here, the coefficient of $v^2$ $(a)$ is $1$ , the coefficient of $v$ $(b)$ is $9$ , and the constant term $(c)$ is $20$ .
Find Multiplying Numbers: Find two numbers that multiply to the constant term $c$ and add up to the coefficient of $v$ $b$ . We need to find two numbers that multiply to $20$ and add up to $9$ . The numbers $4$ and $5$ satisfy these conditions because $4 \times 5 = 20$ and $4 + 5 = 9$ .
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 $(v + 4)(v + 5)$ , because when we expand this, we get $v^2 + 4v + 5v + 20$ , which simplifies to $v^2 + 9v + 20$ .