Factor. h^2 + 10h + 21 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is h^2 + 10h + 21. 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 10. The coefficient c is the constant term, which is 21.Find Multiplying Numbers: Find two numbers that multiply to c (21) and add up to b (10). We need to find two numbers that multiply together to give 21 and add together to give 10. The numbers 3 and 7 satisfy these conditions because 3 * 7 = 21 and 3 + 7 = 10.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (h + 3)(h + 7) because these two binomials multiply to give the original quadratic expression h^2 + 10h + 21.

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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 + 10h + 21

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is $h^2 + 10h + 21$ . 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 $10$ . The coefficient $c$ is the constant term, which is $21$ .
Find Multiplying Numbers: Find two numbers that multiply to $c$ ( $21$ ) and add up to $b$ ( $10$ ). $\newline$ We need to find two numbers that multiply together to give $21$ and add together to give $10$ . The numbers $3$ and $7$ satisfy these conditions because $3 \times 7 = 21$ and $3 + 7 = 10$ .
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 $(h + 3)(h + 7)$ because these two binomials multiply to give the original quadratic expression $h^2 + 10h + 21$ .