Identify Quadratic Expression: Identify the quadratic expression to be factored. The given expression is x^2 + 15x + 54. We need to find two numbers that multiply to give the constant term (54) and add up to give the coefficient of the x term (15).Find Multiplying Numbers: Find two numbers that multiply to 54 and add up to 15. The numbers 6 and 9 satisfy both conditions: 6 * 9 = 54 and 6 + 9 = 15.Write as Binomials: Write the expression as a product of two binomials. The expression x^2 + 15x + 54 can be factored as (x + 6)(x + 9).Check Factored Form: Check the factored form by expanding it to ensure it matches the original expression. (x + 6)(x + 9) = x^2 + 9x + 6x + 54 = x^2 + 15x + 54, which matches the original expression.

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$x^{2}+15 x+54$

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Algebra 1

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x^{2}+15 x+54

Identify Quadratic Expression: Identify the quadratic expression to be factored. $\newline$ The given expression is $x^2 + 15x + 54$ . We need to find two numbers that multiply to give the constant term ( $54$ ) and add up to give the coefficient of the $x$ term ( $15$ ).
Find Multiplying Numbers: Find two numbers that multiply to $54$ and add up to $15$ . The numbers $6$ and $9$ satisfy both conditions: $6 \times 9 = 54$ and $6 + 9 = 15$ .
Write as Binomials: Write the expression as a product of two binomials. $\newline$ The expression $x^2 + 15x + 54$ can be factored as $(x + 6)(x + 9)$ .
Check Factored Form: Check the factored form by expanding it to ensure it matches the original expression. $\newline$ $(x + 6)(x + 9) = x^2 + 9x + 6x + 54 = x^2 + 15x + 54$ , which matches the original expression.