1. Lesson 10.1: Adding/subtracting Polynomials
Monomial: An expression with one term
Ex. a) 2 b) 3x c)-12x2y3
Binomial: An expression with two terms
Ex. a) x b) 2xy + 7ab
Trinomial: An expression with three terms
Ex. 7x2 + 5x - 7
Polynomial: An expression that is the sum of terms (one or more terms)
Ex. 5x + 7y + 15xy – 11z

2. Standard Form: Polynomials written in decreasing order of the variable
Standard Form NOT Standard form
3x2 – 2x x2 –2x
2x3y +4x2y2 – 3xy3 – x2y2 – x3y –3xy3
Coefficient: Number multiplied by a variable in a term
Ex. 3xy coefficient is 3
Leading coefficient: coefficient of first term of a polynomial written in standard form.
Ex. -5x2 + 7x – L.C. = -5

3. Constant: a term with no variables
Ex. 8
Examples: Write in standard form, determine coefficients, leading coefficient, and constant
4 – x + 2x3 2) -9x + 2 3)
2x3 – x + 4
Coeff= 2, -1
LC = 2
Constant = 4
Coeff= -9, 2
LC = -9
Constant = 2
LC = 2
Constant = -7
2x3 + 5x2 – 3x -7
Coeff= 2m 5m –3m -7

4. Degree of a term: exponent of variable
Degree of polynomial: largest degree of the terms
Can classify polynomial by terms (monomial, binomial, trinomial, polynomial) or by degree.
Degree classifications
Degree Classification Example
Constant
Linear x + 7
Quadratic x2 – 5x + 2
Cubic x3 - 1
Quartic x4 –x3 –7x2+2x-3

5. Classify by degree and number of terms.)
3) )
Monomial
Constant
Monomial
Linear
Polynomial
Cubic
Binomial
Quadratic

6. To add/subtract polynomials:
- Use commutative and associative props. to
group like terms
- Combine like terms
**** Remember to change subtraction to adding the opposite.

8. -8x3 +(-9x2)+ 0x + 2
0x x2 + 2x + 4
+ -3x3 + 4x x + -1
-11x3 + 3x2 + 2x +5

13. Homework
p. 580, #19-30 all,#32-62 evens, #63-64