Factor. s^2 + 10s + 21 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is s^2 + 10s + 21. Here, the coefficient of s^2 (a) is 1, the coefficient of s (b) is 10, and the constant term (c) is 21.Find Multiplying Numbers: Find two numbers that multiply to give the constant term (c = 21) and add up to the coefficient of s (b = 10). We need to find two numbers m and n such that m * n = 21 and m + n = 10.Determine Factor Pair: Determine the pair of factors that meet the criteria. The numbers 3 and 7 multiply to give 21 (3 * 7 = 21) and add up to 10 (3 + 7 = 10). Therefore, m = 3 and n = 7 are the numbers we are looking for.Write Factored Form: Write the factored form of the quadratic expression using the numbers found. The factored form of the expression s^2 + 10s + 21 is (s + 3)(s + 7).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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s^2 + 10s + 21

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $s^2 + 10s + 21$ . Here, the coefficient of $s^2$ ( $a$ ) is $1$ , the coefficient of $s$ ( $b$ ) is $10$ , and the constant term ( $c$ ) is $21$ .
Find Multiplying Numbers: Find two numbers that multiply to give the constant term $c = 21$ and add up to the coefficient of $s$ $b = 10$ . We need to find two numbers $m$ and $n$ such that $m \times n = 21$ and $m + n = 10$ .
Determine Factor Pair: Determine the pair of factors that meet the criteria. $\newline$ The numbers $3$ and $7$ multiply to give $21$ ( $3 \times 7 = 21$ ) and add up to $10$ ( $3 + 7 = 10$ ). Therefore, $m = 3$ and $n = 7$ are the numbers we are looking for.
Write Factored Form: Write the factored form of the quadratic expression using the numbers found. $\newline$ The factored form of the expression $s^2 + 10s + 21$ is $(s + 3)(s + 7)$ .