Factor. f^2 + 10f + 21 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression f^2 + 10f + 21. Compare f^2 + 10f + 21 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 10, and c = 21.Find Multiplying Numbers: Find two numbers that multiply to c (21) and add up to b (10). We need to find two numbers m and n such that m * n = 21 and m + n = 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 numbers found in Step 2. The factored form of the quadratic expression is (f + m)(f + n), where m and n are the numbers found in Step 2. Substitute m = 3 and n = 7 into the factored form to get (f + 3)(f + 7).

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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f^2 + 10f + 21

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $f^2 + 10f + 21$ . Compare $f^2 + 10f + 21$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find Multiplying Numbers: Find two numbers that multiply to $c (21)$ and add up to $b (10)$ . We need to find two numbers $m$ and $n$ such that $m \times n = 21$ and $m + n = 10$ . 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 numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(f + m)(f + n)$ , where $m$ and $n$ are the numbers found in Step $2$ . $\newline$ Substitute $m = 3$ and $n = 7$ into the factored form to get $(f + 3)(f + 7)$ .