Factor the following trinomial. \[ x^{2}+15 x+54 \] Select the correct choice below and, if \( n \) A. \( x^{2}+15 x+54=\square \) (Type your an B. The polynomial is prime.

To factor the trinomial \( x^{2}+15x+54 \), we need to find two numbers that multiply to \( 54 \) (the constant term) and add up to \( 15 \) (the coefficient of \( x \)). The numbers \( 6 \) and \( 9 \) fit perfectly because \( 6 \times 9 = 54 \) and \( 6 + 9 = 15 \). Therefore, the factored form is: \[ x^{2}+15x+54 = (x+6)(x+9) \] --- Did you know that factoring trinomials is a crucial skill in algebra that helps in simplifying problems and solving equations without needing a calculator? Mastering this skill opens doors to higher math concepts like quadratic equations and polynomials! Additionally, a common mistake when factoring is not considering negative numbers. In this case, if you were looking for numbers that multiply to a negative \( 54 \), you might be tempted to find \( -6 \) and \( -9 \). Always be sure to check the signs of the factors that you are using to add up to the correct coefficient!