Transcript Do Now 3/20/07 - Howell Township Public Schools

Do Now 2/22/10
• Copy HW in your planner.
– Text p. 557, #4-28 multiples of 4, #32-35 all
• In your notebook on a new page define the
parts of the expression below. Use the
following words: terms, coefficients, constants,
exponents
-3x² + 2x + 8
Chapter 9 “Polynomials and Factoring”
• (9.1) Add and subtract polynomials
• (9.2) Multiply polynomials
• (9.3) Find special products of polynomials
• (9.4) Solve polynomial equations in factored form
• (9.5) Factor x² + bx + c
• (9.6) Factor ax² + bx + c
• (9.7) Factor special products
• (9.8) Factor polynomials completely
Parts of an Expression
Coefficient
the number part
of the term (negative
sign included)
-3x² + 2x + 8
Terms
of the expression
Constant
Term that has
no variable
Objective
• SWBAT add and subtract polynomials
Section 9.1 “Add and Subtract Polynomials”
Monomial
a number, a variable, or the product of a
number and one or more variables with whole
number exponents
-3x
Degree = 1
Degree = 6
x³yz²
7
Degree = 0
Degree of a Monomial
the sum of the exponents of
the variables in the monomial
Polynomial
a monomial, or the sum (or difference) of monomials
Degree = 1
Degree = 0
Degree = 3
–3x +7 – x³
Write a
polynomial with
exponents
decreasing
from left to right.
Degree of a Polynomial
the greatest degree of its terms
-1
Leading Coefficient the coefficient of the first term when
exponents are decreasing from left to right.
Types of Polynomials
Binomial
Trinomial
polynomial with 2 terms
polynomial with 3 terms
4 – 3x
2x³+ x – 7
To Be or Not To Be a Polynomial…
14 – 3x
Yes; 1st degree binomial
4x³
Yes; 3rd degree monomial
-3
2y
9 + 3x² + 2yz³
n
6x + 2x
No; negative exponent
Yes; 4th degree trinomial
No; variable exponent
Add Polynomials
Like Terms
terms that have
the same variable
(2x³ – 5x² + x) + (2x² + x³ – 1)
You can add polynomials using the vertical or horizontal format.
Vertical Format
Horizontal Format
(2x³ + x³) + (2x² – 5x²) + x – 1
2x³ – 5x² + x
x³ + 2x²
–1
3x³ – 3x² + x – 1
3x³ – 3x² + x – 1
Subtract Polynomials
Like Terms
terms that have
the same variable
(4n² + 5) – (-2n² + 2n – 4)
You can subtract polynomials using the vertical or horizontal format.
Vertical Format
4n²
Horizontal Format
+5
– +(2n²
(-2n² +2n
-2n +
– 4)
6n² – 2n + 9
(4n² + 2n²) – 2n + (5 + 4)
6n² – 2n + 9
Adding and Subtracting Polynomials
(5a 2  3)  (8a 2 1)
(5a 2  8a 2 )  (3  1)
13a 2  4
(n2  2n)  (2n3  n2  n  12)
 2n3  (n 2  n 2 )  (2n  n)  12
 2n3  n  12
Simplifying Polynomials in Geometry
• What is the perimeter of the
trapezoid?
Perimeter is the
distance around a figure.
Add together each of the sides.
3x – 2
3x - 2 + 2x + 2x + 1 + 5x - 2
(reorder terms)
2x
2x + 1
5x – 2
3x + 2x + 2x + 5x – 2 – 2 + 1
(combine like terms)
12x – 3
Homework
Text p. 557,
#4-28 multiples of 4, #32-35 all