Factor. f^2 + 10f + 9 ____

Identify Variables: Identify a, b, and c in the quadratic expression f^2 + 10f + 9. Compare f^2 + 10f + 9 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 10, and c = 9.Find Two Numbers: Find two numbers that multiply to c (which is 9) and add up to b (which is 10). We are looking for two numbers whose product is 9 and whose sum is 10. The numbers 1 and 9 satisfy these conditions because: 1 * 9 = 9 (product is c) 1 + 9 = 10 (sum is b)Write Factored Form: Write the factored form using the two numbers found in Step 2. The quadratic expression can be factored as (f + 1)(f + 9).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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f^2 + 10f + 9

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $f^2 + 10f + 9$ . Compare $f^2 + 10f + 9$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 10$ , and $c = 9$ .
Find Two Numbers: Find two numbers that multiply to $c$ (which is $9$ ) and add up to $b$ (which is $10$ ). $\newline$ We are looking for two numbers whose product is $9$ and whose sum is $10$ . $\newline$ The numbers $1$ and $9$ satisfy these conditions because: $\newline$ $1 \times 9 = 9$ (product is $c$ ) $\newline$ $9$ $0$ (sum is $b$ )
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The quadratic expression can be factored as $(f + 1)(f + 9)$ .