Factor. n^2 + 10n + 9 ____

Identify Coefficients: Identify the coefficients for n^2, n, and the constant term in the quadratic expression n^2 + 10n + 9. Comparing n^2 + 10n + 9 with the standard quadratic form ax^2 + bx + c, we find that a = 1 (coefficient of n^2), b = 10 (coefficient of n), and c = 9 (constant term).Find Multiplying Numbers: Determine two numbers that multiply to c (9) and add up to b (10). We are looking for two numbers that when multiplied give 9 and when added give 10. The numbers 1 and 9 satisfy these conditions because 1 * 9 = 9 and 1 + 9 = 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 (n + 1)(n + 9), since these two binomials multiply to give the original quadratic expression n^2 + 10n + 9.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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n^2 + 10n + 9

Identify Coefficients: Identify the coefficients for $n^2$ , $n$ , and the constant term in the quadratic expression $n^2 + 10n + 9$ . Comparing $n^2 + 10n + 9$ with the standard quadratic form $ax^2 + bx + c$ , we find that $a = 1$ (coefficient of $n^2$ ), $b = 10$ (coefficient of $n$ ), and $c = 9$ (constant term).
Find Multiplying Numbers: Determine two numbers that multiply to $c (9)$ and add up to $b (10)$ . We are looking for two numbers that when multiplied give $9$ and when added give $10$ . The numbers $1$ and $9$ satisfy these conditions because $1 \times 9 = 9$ and $1 + 9 = 10$ .
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 $(n + 1)(n + 9)$ , since these two binomials multiply to give the original quadratic expression $n^2 + 10n + 9$ .