1. 8-1 Adding and subtracting Polynomials
Goals:
Add and subtract polynomials.
Eligible Content: A

2. Vocabulary
Polynomial – a mathematical expression consisting of a sum of terms. Each term is the product of a constant and one or more variables raised to a positive or zero power.
Examples:

3. vocabulary
Standard Form – the terms are in descending order of exponents.

4. vocabulary
Degree – the largest exponent in the polynomial.

5. vocabulary Constant – degree is zero. Linear – degree is one.
Quadratic – degree is two.
Cubic – degree is three.
Quartic – degree is four.

6. vocabulary
Leading coefficient – the coefficient of the first term when the polynomial is in standard form.

7. vocabulary Monomial – polynomial with one term.
Binomial – polynomial with two terms.
Trinomial – polynomial with three terms.
Anything bigger – polynomial

8. Examples
Give the degree and classify the polynomial by degree and number of terms. -5
¼ x
-9x+2
x2 – 6
-x3 +2x + 1
3x4 +2x3 – x2 +5x – 8
0, constant, monomial
1, linear, monomial
1, linear, binomial
2, quadratic, binomial
3, cubic, trinomial
4, quartic, polynomial

9. Addition
Add like terms!
Put your answer in Standard Form!!

10. examples

11. Find (3x2 + 2x – 1) + (–5x2 + 3x + 4).
A. –2x2 + 5x + 3
B. 8x2 + 6x – 4
C. 2x2 + 5x + 4
D. –15x2 + 6x – 4

12. Find (4x3 + 2x2 – x + 2) + (3x2 + 4x – 8).
A. 5x2 + 3x – 6
B. 4x3 + 5x2 + 3x – 6
C. 7x3 + 5x2 + 3x – 6
D. 7x3 + 6x2 + 3x – 6

13. Subtraction Distribute the negative sign!
Add like terms and put your answer in Standard Form!!

14. examples

15. Find (3x3 + 2x2 – x4) – (x2 + 5x3 – 2x4).
A. 2x2 + 7x3 – 3x4
B. x4 – 2x3 + x2
C. x2 + 8x3 – 3x4
D. 3x4 + 2x3 + x2

16. Find (8y4 + 3y2 – 2) – (6y4 + 5y3 + 9).
A. 2y4 – 2y2 – 11
B. 2y4 + 5y3 + 3y2 – 11
C. 2y4 – 5y3 + 3y2 – 11
D. 2y4 – 5y3 + 3y2 + 7

17. Practice
Page 468 #1-18

18. Homework
Pages #20 – 42 even