What to Expect on the Chapter 3 Exam

· Graphing Polynomials

· Polynomial Division

· Possible Rational Factors

· Synthetic Division

· Remainder Theorem

· Complex Roots, Factors

· Complex Numbers in Synthetic Division

· Complex Conjugates

In graphing polynomials, you will need to find the zeroes [x-intercept], y-intercept, and make a nice, smooth graph of the function. Those zeroes will be determined by the Rational Root Theorem, which determines the only possible rational factors, and from that list you will attempt synthetic division to determine which ones work. At most there will be the same number of factors as the degree of the polynomial.

The Remainder Theorem says that f of a number will equal the remainder if that number is put into synthetic division. So f(5) will be the remainder when 5 is put into synthetic division.

Polynomial division works like regular division, only with variables in it. If the degree of the guy on the outside is 1, then you can use synthetic division. If it is more than one, then you can’t.

The total number of complex roots is the degree of the polynomial. For example, if the polynomial is of degree 7, then there may be 3 rational real complex zeros, 2 irrational real complex zeroes, and 2 non-real complex zeroes. Non-real complex zeroes always come in conjugate pairs.

Complex numbers are in the form z = a + bi, where a is the real component and b is the non-real component. If b = 0, then the number is a real complex. If b is not 0, then the number is a non-real complex. Complex conjugates are in the form a + bi and a – bi.