Factor. w^2 + 7w + 10 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is w^2 + 7w + 10. Here, the coefficient of w^2 (a) is 1, the coefficient of w (b) is 7, and the constant term (c) is 10.Find Multiplying Numbers: Find two numbers that multiply to the constant term (c) and add up to the coefficient of w (b). 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 * 5 = 10 and 2 + 5 = 7.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (w + 2)(w + 5), because when we expand this, we get w^2 + 2w + 5w + 10, which simplifies to w^2 + 7w + 10.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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w^2 + 7w + 10

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $w^2 + 7w + 10$ . Here, the coefficient of $w^2$ $(a)$ is $1$ , the coefficient of $w$ $(b)$ is $7$ , and the constant term $(c)$ is $10$ .
Find Multiplying Numbers: Find two numbers that multiply to the constant term $c$ and add up to the coefficient of $w$ $b$ . 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 the previous step. $\newline$ The factored form of the quadratic expression is $(w + 2)(w + 5)$ , because when we expand this, we get $w^2 + 2w + 5w + 10$ , which simplifies to $w^2 + 7w + 10$ .