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Warm up

Warm up. Polynomials. Objectives Add, subtract, multiply, divide and factor polynomials Simplify and solve equations involving roots, radicals, and rational exponents Perform operations with complex numbers. 5.1 Monomials. Vocabulary Monomial – expression with one term

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Warm up

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  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 2. .000092 • 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 2. -16p5 + (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 1. (+-) √(16x6) 2. - √(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

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