1. 8.1 Adding and Subtracting Polynomials
Objective: SWBAT add and subtract polynomials and classify polynomials by degree and terms.

2. Mini Quiz 1
1. What is the solution set of the inequality 5 – |x + 4| ≤ -3
a)-2 ≤ x ≤ 6 b) x ≤ -2 or x ≥ 6
c) -12 ≤ x ≤ 4 d) x ≤ -12 or x ≥ 4
The lengths of the sides of a triangle are y, y + 1, and 7 centimeters. If the perimeter is 56 centimeters, what is the value of y? a) 24 b) 25 c) 31 d) 32
What is the solution to the inequality x – 5 > 14?
a) x > 9 b) x > 19 c) x < 9 d) x < 19

3. CAHSEE Review Mean – Average (that’s mean!) Median – Middle Number
Mode – Most Often

4. Overview Classifying Polynomials
By Degree
Number of Terms
Adding Polynomials (combine like terms)
Subtracting Polynomials (distribute and combine like terms)

5. Quick Review x y x2 y3 x2y Sort the following terms:
2x 5y y x x y3
4x2 7x2y yx y x2 x y x2 y3
x2y

6. Monomials…Polynomials
Monomial – is a number, a variable, or a product of a number and variable(s)
Examples:
Polynomial – is a sum of one or more monomials
5; y; 8x2
5 + 7x; y – 4x + 24y2 ; 8y2 – 4xy + x2

7. Another Standard Form…
…the polynomial has the degrees placed in descending order (largest to smallest)
2x3 + 5x2 – 4x + 7
Degree (of polynomial)
Leading coefficient
Constant term
Terms are separated by the +/- signs
How many terms does this polynomial have? 4

8. Name that Degree 2x3 9x + 4x2 – 3 28y + 2y3 + 7y5 – 3x
-2xy + 3xy2 – xy3
-3xyz – 4yz3 – x2y2z 3 2 5 4 1 1

9. Classified by # of terms
Name that polynomial!
Polynomial
Degree
Classified by Degree
# of terms
Classified by # of terms 6
Constant 1
Monomial
-2x – 4 1
Linear 2
Binomial
-x x 2
Quadratic 3
Trinomial
– 8x2 +4x3 3
Cubic 2
Binomial
3x+2x4 –1+3x2 4
Quartic 4
Polynomial

10. Adding and Subtracting Polynomials
Steps:
Distribute (sign changes when it’s minus)
Combine Like Terms
Simplify: (7x3 – 3x2 + 5) – (2x3 – 5x + 7)
7x3 – 3x2 + 5
5x3
– 2x3 + 5x – 7
- 3x2
+ 5x
- 2

11. Adding and Subtracting Polynomials
3x2 + 2x + 1
1. (2x2 + x - 5) + (x + x2 + 6)
2. (3x2 - 5x + 3) - (2x2 - x – 4)
3. (-4x3 + x - 3x2) - (-x2 + 2 – 9x)
4. (5x3 – x + 2x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3)
5. (-2x3 - x + 5x2 + 8) - (-2x x) + (7x + 4x2)
x2 – 4x + 7
-4x3 – 2x2 + 10x + 2
4x3 + 9x2 – 5x + 6
9x2 + 3x + 12

12. Wrap Up Classifying Polynomials
By Degree
Constant (0)
Linear (1)
Quadratic (2)
Cubic (3)
Quartic (4)
Adding Polynomials (combine like terms)
Subtracting Polynomials
HW: P #1-39 odd
DLUQ: When you distribute, when does the sign changes?
- Number of Terms
Monomial (1)
Binomial (2)
Trinomial (3)
Polynomial (4+)