2 Polynomials Objectives Add, subtract, multiply, divide and factor polynomialsSimplify and solve equations involving roots, radicals, and rational exponentsPerform operations with complex numbers
3 5.1 Monomials Vocabulary Monomial – expression with one term Constants – monomials that contain no variablesCoefficient – the numerical factor of a variableDegree – the sum of the exponents of the variablePower – expression of the form xnScientific 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+nQuotient of powers – (am/an) = am-nPower of a power – (am)n = amxn
6 5.1 Examples continued Express each number in scientific notation 1. 4,560,000Evaluate3. (5 x 103)(7 x 108)4. (1.8 x 10-4)(4 x 107)
7 5.2 warm upTop of page 229How 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 termsTrinomial – three unlike terms
9 5.2 ExamplesDetermine whether each expression is a polynomial, state the degree.1. C4 – 4sqrt(c) + 18p5 + (3/4)p2q7Simplify3. (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 upTop of page 233What 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?
17 5.6 Radical ExpressionsA radical expression is in simplified form when the following conditions are met.The index n is as small as possibleThe radical contains no factors that are the nth powers of an integer or polynomialThe radical contains no fractionsNo radicals appear in the denominator