1. Warm up

2. Polynomials Objectives
Add, subtract, multiply, divide and factor polynomials
Simplify and solve equations involving roots, radicals, and rational exponents
Perform operations with complex numbers

3. 5.1 Monomials Vocabulary Monomial – expression with one term
Constants – monomials that contain no variables
Coefficient – the numerical factor of a variable
Degree – the sum of the exponents of the variable
Power – expression of the form xn
Scientific notation – a x 10n where 1< a < 10, it is used to express very large and very small numbers

4. Rules for exponents Negative exponents a–n = (1/an) and (1/a-n) = an
Product of powers – am x an = am+n
Quotient of powers – (am/an) = am-n
Power of a power – (am)n = amxn

5. 5.1 Examples Simplify 1. (-2a3b)(-5ab4) 2. (s2/s10) 3. (b2)4
4. (-3c2d5)3
5. (-2a/b2)5
6. (x/3)-4
7. (-3a5y/a6yb4)5

6. 5.1 Examples continued Express each number in scientific notation
1. 4,560,000
Evaluate
3. (5 x 103)(7 x 108)
4. (1.8 x 10-4)(4 x 107)

7. 5.2 warm up
Top of page 229
How can polynomials be applied to financial situations?
What is meant by “tuition increases at a rate of 4% per year?
Will the amount of the tuition increase be the same each year?

8. 5.2 Polynomials Vocabulary Polynomial – a monomial or sum of monomials
Binomial – two unlike terms
Trinomial – three unlike terms

9. 5.2 Examples
Determine whether each expression is a polynomial, state the degree.
1. C4 – 4sqrt(c) + 18
p5 + (3/4)p2q7
Simplify
3. (2a3 + 5a -7) – (a3 – 3a + 2)
4. –y(4y2 + 2y – 3)
5. (2p + 3)(4p + 1)
6. (a2 + 3a – 4)(a + 2)

10. 5.3 warm up
Top of page 233
What does the expression (x/2) shown in the figure represent?
What happens to the width of the pipe opening as the length of the pipe increases?

11. 5.3 Dividing polynomials Simplify polynomial divided by a monomial
Synthetic division
Examples
(5a2b – 15ab3 + 10a3b4)/(5ab)
(X2 – 2x – 15)/(x – 5)
(x3 – 4x2 + 6x – 4)/(x-2)
(4y4 – 5y2 + 2y + 4)/(2y-1)

12. 5.4 Factoring polynomials
Factoring Techniques Write rules page 239
GCF
Difference of 2 squares
Sum of two cubes
Difference of two cubes
Perfect square trinomials
General trinomials
Grouping

13. 5.4 warm up Factor 1. 10a3b2 + 15a2b -5ab3 2. x3 + 5x2 – 2x – 10
3. 3y2 - 2y – 5
4. 5mp2 – 45m
5. X3y3 + 8
6. 64x6 – y6
7. Simplify (a2 – a – 6)/(a2 + 7a + 10)

14. 5.5 Roots of real numbers Warm up p. 244 #57 and #58 Examples
√(q3+5)4
3. 5√(243a10b15)
4. √-4
5. 6√t6
6. 5√(243(x+2)15)

15. 5.6 warm up
Page 248 #60

16. 5.5 Roots of real numbers
Examples

17. 5.6 Radical Expressions
A radical expression is in simplified form when the following conditions are met.
The index n is as small as possible
The radical contains no factors that are the nth powers of an integer or polynomial
The radical contains no fractions
No radicals appear in the denominator

18. 5.6 Examples
Overhead projector