The divisor represented by the synthetic division notation you provided, which is written as 5 5 x 5 x 5, is referring to a polynomial being divided by the binomial (x – 5). In synthetic division, the coefficients of the polynomial are aligned with the value being used as the divisor, which in this case uses the number 5.
Here’s a breakdown of how we determine this:
- The numbers written before involve the coefficients of the polynomial. If we interpret this as x^n + ax^(n-1) + … + z, where ‘n’ is the degree of the polynomial, the value of ‘5’ indicates that we’re looking at (x – 5) as the divisor.
- When performing synthetic division, the root of the divisor (in this case, 5) is placed to the left of the synthetic division bar.
- The process of synthetic division shows how the polynomial is evaluated at this specific point, ultimately determining its behavior as we divide.
To summarize, based on synthetic division, the divisor is (x – 5). This method simplifies the division process and makes it easier to analyze polynomial equations.