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Warm up

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**Polynomials Objectives**

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

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**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

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**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

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**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

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**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)

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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?

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**5.2 Polynomials Vocabulary Polynomial – a monomial or sum of monomials**

Binomial – two unlike terms Trinomial – three unlike terms

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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)

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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?

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**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)

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**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

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**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)

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**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)

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5.6 warm up Page 248 #60

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5.5 Roots of real numbers Examples

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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

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5.6 Examples Overhead projector

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