# Chapter 6.6-6.9 Test Outline

From Huben's Wiki

6.6: factoring polynomials

- n terms
- greatest common factor

- 2 terms
- difference of squares
- difference of cubes
- sum of cubes

- 3 terms
- perfect square trinomials
- general trinomials

- 4 or more terms: grouping
- using these in combination

6.7: remainder and factor theorems

- synthetic substition: f(a) = f(x) / (x - a)
- remainder theorem: f(x) / (x-a) has remainder f(a)
- factor theorem: (x - a) is a factor of f(x) iff f(a) = 0

6.8: roots and zeros

- Let f(x) be a polynomial function. Then:
- c is a zero of f(x)
- x-c is a factor of f(x)
- c is a root or solution of f(x) = 0
- (c, 0) is an x-intercept of f(x)

- fundamental theorem of algebra
- every polynomial of degree 1 or greater has at least one root in the complex numbers
- corollary: a polynomial of degree n has n roots in the complex numbers

- Descartes rule of signs
- complex conjugates theorem
- complex roots come in conjugate pairs

- use these to find all roots
- write polynomials using roots

6.9: rational zero theorem

- find all possible rational roots
- find rational zeros
- find remaining zeros