I reviewed solutions of polynomial equations with Matthew during the first session and we began the test during the second session. Since he was learning virtually and did not have his text with him, I gave him certain formulas which he would have use of if he had been there in person. The topics on the test included forming polynomials from their solutions and finding zeros by factoring. Matthew did not finish the test but will continue to work on it during the next session. There was no assignment.

Joshua continued to work on his test while I supervised. There were quesions on the test requiring the student to write the generic rules for both arithmetic and geometric series. There were also problems in which the student was supposed to find the sums of both finite and infinite series. There was no assignment.

I reviewed several problems with Matthew in final preparation for his chapter test on polynomials next week. We factored polynomials, found their zeros, and built polynomials from their zeros. The type of polynomials he was able to factor included factoring by grouping and fourth-degree polynomials in the quadratic form. There was no assignment.

Joshua and I worked together to solve problems including finding the sums of arithmetic and geometric series. We used formulas provided in order to save work in evaluating series expressed in sigma notation. We also evaluated infinite series that were convergent and those divergent series that did not have a sum. There was no assignment.

I worked with Matthew to solve various problems that were similar to standardized test questions since he told me that he hadn't taken the SAT or ACT tests yet. We started by simplifying a rational algebraic expression using the rules of exponents. From there, I reviewed how cubic equations can be broken down, followed by constructing a polynomial from its roots, including imaginary ones. We finished up the session by finding real roots of a polynomial and evaluating a polynomial at a given point using synthetic substitution.
In the second session, we started by using an extra practice session and revisiting the properties of exponents along with expanding a binomial raised to the third power. There was no assignment.

I worked with Joshua to convert an arithmetic series into a sum formula in order to sum a given number of terms. We also converted a geometric series into sigma notation so that we could apply the sum formula for geometric series. After finding the sum in two different ways, we were out of time. There was no assignment.

I continued to work with Matthew to review procedures for finding the zeros of polynomials. We used The fundamental theorem of algebra and the rational root theorem to generate possible solutions of a
polynomial and to test the solutions using synthetic division and checking for zeros. We also built polynomials from the list of solutions. There was no assignment.

I gave Joshua my practice test to help him prepare for the test on series and sequences. We covered the operation of finding a specific term in a sequence or series along with finding the sums of series using sigma notation. We will continue to work on the practice test the next time we meet. There was no assignment.

I worked with Matthew on some problems about exponents and rational expressions. We then reviewed polynomial long division and synthetic division. Also, I checked his ability to add, subtract, multiply, and divide polynomials. We concluded with some factoring of polynomials. There was no assignment.

The plan was to review with Matthew about exponents and fractions, multiplication of three binomials, and factoring polynomials completely. Unfortunately, Matthew was not available for either virtual or in-person instruction. There was no assignment.