This document discusses exponents, polynomials, and factoring. It defines exponents as the number of times a factor is present in a product. Polynomials are algebraic expressions with variables and constant numbers that have terms, coefficients, degree, and constant and leading terms. Factoring involves finding the greatest common factor and largest exponent to take out of an equation. Examples show factoring by taking out common factors and using the grouping method.

1. Exponents, Polynomials, and
Factoring
By: Christina Blunden

2. Exponents
An exponent is the number of
times a factor is present in a
product.

3. Exponents
a n
This is an example of a number with an
exponent.
Base: In this example the base is letter a.
Exponent: In this example the exponent is
letter n.

4. Exponents
8 represents 8x8x8 which
3
equals 512
Any number with an exponent
of zero is 1.
EX: 5 0 = 1, 3 0 =1

5. Exponents
For the following questions
give the answer.
5 3
7 5
9 0

6. Exponents
Answers to previous questions:
5 3= 5x5x5 = 125
7 5= 7x7x7x7x7 = 16807
9 0= 1

7. Polynomials
Polynomials are algebraic
expressions that have variables
as well as constant numbers.
Ex: 3x 3+4x2-2x+5

8. Polynomials
3x3+4x2-2x+5
Coefficients: The real numbers in front of
the variable. Ex: 3,4,-2,5
Terms: The parts separated by the plus and
minus signs. Ex: 3x3,4x2,-2x,5
Leading Coefficient: The first number in the
polynomial. Ex: 3

9. Polynomials
3x3+4x2-2x+5
Constant Term: The number without the variable. Ex: 5
Degree: The degree of the polynomial is the highest exponent.
Ex: the degree of this polynomial is 3
Descending Order: The exponents decrease from right to left
when written in order. Ex: 3,2,1,0

10. Polynomials
Find the terms for each question below.
5x3-4x2+9x+7
-7z5+2z4-5z3-8z2+3z-4

11. Polynomials
Answers to previous questions. Find the
terms
5x3-4x2+9x+7 The terms for this
polynomial are 5x3, -4x2, 9x, 7
-7z5+2z4-5z3-8z2+3z-4 The terms for
this polynomial are -7z5, 2z4, -5z3, -8z2,
3z, -4

12. Polynomials
Find the degree of each polynomial listed.
5x3-4x2+9x+7
-7z5+2z4-5z3-8z2+3z-4

13. Polynomials
Answers to the previous slide. Find the
Degree
5x3-4x2+9x+7 The degree of this
polynomial is 3
-7z5+2z4-5z3-8z2+3z-4 The degree of
this polynomial is 5

14. Factoring
When factoring find the greatest common
factor and the largest exponent to take
out of the equation. Take out the largest
common factor.

15. Factoring
Factor this equation: 15+10x-5x2
5(3+2x-x2)

16. Factoring
Factor this equation: 12x2y2-20x3y
4x2y(3y-5x)

17. Factoring
Factoring by Grouping:Some polynomials
have common binomial factors that can
be removed in this process

18. Factoring
Factor this by grouping: x3+3x2-5x-15
(x3+3x2)+(-5x-15)
x2(x+3) - 5(x+3)
(x+3)(x2-5)

19. Works Cited
All information and examples from College
Algebra Graphs and Models Fourth Edition
Authors: Bittinger, Beecher, Ellenbogen, Penna