Warm up Polynomials Objectives 1. Add, subtract, multiply, divide and factor polynomials 2. Simplify...
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Transcript of Warm up Polynomials Objectives 1. Add, subtract, multiply, divide and factor polynomials 2. Simplify...
Warm up
Polynomials
Objectives1. Add, subtract, multiply, divide and factor
polynomials2. Simplify and solve equations involving
roots, radicals, and rational exponents3. Perform operations with complex
numbers
5.1 MonomialsVocabulary
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
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
5.1 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
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)
5.2 warm up
Top of page 229
1. How can polynomials be applied to financial situations?
2. What is meant by “tuition increases at a rate of 4% per year?
3. Will the amount of the tuition increase be the same each year?
5.2 Polynomials
Vocabulary Polynomial – a monomial or sum of
monomials Binomial – two unlike
terms Trinomial – three
unlike terms
5.2 Examples
Determine whether each expression is a polynomial, state the degree.
1. C4 – 4sqrt(c) + 182. -16p5 + (3/4)p2q7
Simplify3. (2a3 + 5a -7) – (a3 – 3a + 2)4. –y(4y2 + 2y – 3)5. (2p + 3)(4p + 1)6. (a2 + 3a – 4)(a + 2)
5.3 warm up
Top of page 233
1. What does the expression (x/2) shown in the figure represent?
2. What happens to the width of the pipe opening as the length of the pipe increases?
5.3 Dividing polynomials
Simplify polynomial divided by a monomial
Synthetic divisionExamples1. (5a2b – 15ab3 + 10a3b4)/(5ab)2. (X2 – 2x – 15)/(x – 5)3. (x3 – 4x2 + 6x – 4)/(x-2)4. (4y4 – 5y2 + 2y + 4)/(2y-1)
5.4 Factoring polynomials
Factoring Techniques Write rules page 239
1. GCF
2. Difference of 2 squares
3. Sum of two cubes
4. Difference of two cubes
5. Perfect square trinomials
6. General trinomials
7. Grouping
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)
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)
5.6 warm up
Page 248 #60
5.5 Roots of real numbers
Examples
46 3
10 155
156 6 5
1. 16 2. 5
3. 24 4. 4
5. 6. 243 2
x q
a b
t x
5.6 Radical Expressions A radical expression is in simplified form
when the following conditions are met.
1. The index n is as small as possible
2. The radical contains no factors that are the nth powers of an integer or polynomial
3. The radical contains no fractions
4. No radicals appear in the denominator
5.6 Examples
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