Factor. h^2 + 12h + 20 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is h^2 + 12h + 20. In the standard form of a quadratic expression ax^2 + bx + c, the coefficient a is the coefficient of h^2, which is 1. The coefficient b is the coefficient of h, which is 12, and the coefficient c is the constant term, which is 20.Find Numbers: Find two numbers that multiply to give c (20) and add to give b (12). We need to find two numbers that multiply together to get 20 and add up to 12. The numbers 4 and 5 satisfy these conditions because 4 * 5 = 20 and 4 + 5 = 12.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression will be (h + m)(h + n), where m and n are the numbers found in the previous step. Substituting 4 for m and 5 for n, we get the factored form (h + 4)(h + 5).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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h^2 + 12h + 20

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is $h^2 + 12h + 20$ . In the standard form of a quadratic expression $ax^2 + bx + c$ , the coefficient $a$ is the coefficient of $h^2$ , which is $1$ . The coefficient $b$ is the coefficient of $h$ , which is $12$ , and the coefficient $c$ is the constant term, which is $20$ .
Find Numbers: Find two numbers that multiply to give $c (20)$ and add to give $b (12)$ . We need to find two numbers that multiply together to get $20$ and add up to $12$ . The numbers $4$ and $5$ satisfy these conditions because $4 \times 5 = 20$ and $4 + 5 = 12$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression will be $(h + m)(h + n)$ , where $m$ and $n$ are the numbers found in the previous step. Substituting $4$ for $m$ and $5$ for $n$ , we get the factored form $(h + 4)(h + 5)$ .