1. -3x² + 2x + 8 Do Now 2/22/12 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

2. 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

3. -3x² + 2x + 8 Parts of an Expression Coefficient Terms Constant
Remember this???
Coefficient
the number part
of the term (negative sign included)
-3x² + 2x + 8
Terms
of the expression
Constant
Term that has
no variable

4. Objective
SWBAT add and subtract polynomials

5. 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 7
Degree = 0
Degree of a Monomial
the sum of the exponents of the variables in the monomial
Degree = 6
x³yz²

6. –3x +7 – x³ Polynomial -1 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.

7. 2x³+ x – 7 4 – 3x Types of Polynomials Binomial Trinomial
polynomial with 2 terms
polynomial with 3 terms
2x³+ x – 7
4 – 3x

8. To Be or Not To Be a Polynomial…
14 – 3x
Yes; 1st degree binomial
4x³
Yes; 3rd degree monomial -3 2y
No; negative exponent
9 + 3x² + 2yz³
Yes; 4th degree trinomial n
6x + 2x
No; variable exponent

9. Add Polynomials (2x³ – 5x² + x) + (2x² + x³ – 1) 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

10. Subtract Polynomials (4n² + 5) – (-2n² + 2n – 4) Like Terms 4n² + 5
terms that have
the same variable
(4n² + 5) –
(-2n² + 2n – 4)
You can subtract polynomials using the vertical or horizontal format.
Vertical Format
Horizontal Format
4n²
(4n² + 2n²) – 2n + (5 + 4)
– (-2n² +2n – 4)
+(2n² -2n + 4)
6n² – 2n + 9
6n² – 2n + 9

11. Adding and Subtracting Polynomials

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 x + 2x x - 2
(reorder terms) 2x
2x + 1
3x + 2x + 2x + 5x – 2 – 2 + 1
(combine like terms)
12x – 3
5x – 2