Transcript A2 Ch 6 Polynomials Notesx

Algebra 2
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Warm Up
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A monomial is an expression that is either a
real number, a variable or a product of real
numbers and variables.
A polynomial is a monomial or the sum of
monomials.
The exponent of the variable in a term
determines the degree of that term.
Standard form of a polynomial has the
variable in descending order by degree.
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The degree of a polynomial is the greatest
degree of any term in the polynomial
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Write each polynomial in standard form and
classify it by degree.
You can write a polynomial as a product of its linear factors
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You can sometimes use the GCF to help factor a
polynomial. The GCF will contain variables
common to all terms, as well as numbers
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If a linear factor of a polynomial is repeated,
the zero is repeated. A repeated zero is called
a multiple zero. A multiple zero has
multiplicity equal to the number of times the
zero occurs.
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page 323 (1-11, 17-35)odd
you do NOT need to graph the functions.
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Two people per worksheet.
Take turns at each step, first partner decides
what you multiply the divisor by, second
partner agrees and does the multiplication,
first partner agrees and does the subtraction,
then switch for next term.
You may do the work on the worksheet,
paper or the white board. If you use the white
board you must have me check EACH answer
as you complete it.
Warm Up:
1. Write a polynomial function in standard
form with zeros at -1, 2 and 5.
2. Use long division to divide:
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3.
Use long division to divide
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Solve for all three roots
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Homework:
page 330 (227-33) odd
page 336 (13 – 31) odd,
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Solve these equations:
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1. x3 + 125 = 0
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2. x4 + 3x2 – 28 = 0
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To find all the roots of a polynomial:
◦ determine the possible rational roots using the
rational root theorem (ao/an)
◦ Use synthetic division to test the possible rational
roots until one divides evenly
◦ Write the factored form and solve for all roots
 Use the quadratic formula if necessary
 You may need to use synthetic division more than once
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Warm Up
Find the polynomial equation in standard
form that has roots at -5, -4 and 3
Find f(-2) for f(x) = x4 – 2x3 +4x2 + x + 1
using synthetic division
Solve x4 – 100 = 0
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Practice Problem:
List all the possible rational roots of
◦ 3x3 + x2 – 15x – 5 = 0
Use synthetic division to determine which of these is
a root
Factor and solve for the rest of the roots of the
equation.
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A third degree polynomial has roots 2 and
√3. Write the polynomial in standard form.
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Homework
p 345 (11-23) odd
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A selection of items in which order does not
matter is called a combination
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homework
p 354 (1-29) odd
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Warm Up
Find the zeros of the function by finding the
possible rational roots and using synthetic
division.
multiply each and write in standard form:
(x + y)2
(x + y)3
(x + y)4
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Notice that each set of coefficients matches a
row of Pascal’s Triangle
Each row of Pascal’s Triangle contains
coefficients for the expansion of (a+b)n
For example, when n = 6 you can find the
coefficients for the expansion of (a+b)6 in the
7th row of the triangle.
Use Pascal’s Triangle to expand (a+b)6
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If the terms of the polynomial have
coefficients other than 1, you can still base
the expansion on the triangle.
Warm up
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To find a particular term of a binomial
expansion you do not need to calculate the
entire polynomial!
Ex: Find the 5th term of (x – 4)8
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Find the 4th term of (x – 3)8
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Chapter 6 Test this Thursday (5th) or Friday
(4th)
Homework: Complete practice test