Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic-like equation, which are the numbers in front of the variables. In this case, the coefficients are 1, -52, and 51. Step Calculation: Coefficients are 1, -52, 51 Step Output: Coefficients: 1, -52, 51Find Factors: Step Title: Find the Factors Concise Step Description: Find two numbers that multiply to 51 (the constant term) and add to -52 (the coefficient of the middle term). Step Calculation: Factors of 51 that add up to -52 are -1 and -51. Step Output: Factors: -1, -51Write Factored Form: Step Title: Write the Factored Form Concise Step Description: Write the factored form of the equation using the factors found in the previous step. Step Calculation: The factored form is (r - 1)(r - 51). Step Output: Factored Form: (r - 1)(r - 51)

Algebra 2

Factor polynomials

Full solution

r^{13}-52 r+51=0

Identify Coefficients: Step Title: Identify the Coefficients $\newline$ Concise Step Description: Identify the coefficients of the quadratic-like equation, which are the numbers in front of the variables. In this case, the coefficients are $1$ , $-52$ , and $51$ . $\newline$ Step Calculation: Coefficients are $1$ , $-52$ , $51$ $\newline$ Step Output: Coefficients: $1$ , $-52$ , $51$
Find Factors: Step Title: Find the Factors $\newline$ Concise Step Description: Find two numbers that multiply to $51$ (the constant term) and add to $-52$ (the coefficient of the middle term). $\newline$ Step Calculation: Factors of $51$ that add up to $-52$ are $-1$ and $-51$ . $\newline$ Step Output: Factors: $-1$ , $-51$
Write Factored Form: Step Title: Write the Factored Form $\newline$ Concise Step Description: Write the factored form of the equation using the factors found in the previous step. $\newline$ Step Calculation: The factored form is $(r - 1)(r - 51)$ . $\newline$ Step Output: Factored Form: $(r - 1)(r - 51)$