1. 10.1/10.2 Adding and Subtracting polynomials; multiplying and factoring.
Objectives: Describe polynomials. Add and subtract polynomials.
Algebra 1 CP – Miss Battaglia

2. Describing Polynomials:
Polynomial: A polynomial is one term or the sum or difference of two or more terms. A polynomial has no variables in a denominator. For a term that has one variable, the degree of a term is the exponent of the variable. x3 – 4x + 5x2 + 7
The degree of a constant is 0.
degree

3. Name Using Number of Terms
The degree of a polynomial is the same as the degree of the term with the highest degree. You can name a polynomial by its degree or by the number of its terms. The polynomials in the chart are in standard form, which means the terms decrease in degree from left to right and no terms have the same degree.
Polynomial
Degree
Name Using Degree
Number of Terms
Name Using Number of Terms
7x + 4 1
Linear 2
Binomial
3x2 + 2x + 1
Quadratic 3
Trinomial
4x3
Cubic
Monomial 5
Constant

4. Example 1
Write each polynomial in standard form. Then name each polynomial by its degree and the number of its terms. a. 5 – 2x b. 3x4 – 4 + 2x c. -2x + 5 – 4x2 + x3

5. Example 2
Find (2x2 – 3x + 4) + (3x2 + 2x – 3)

6. Example 3
Find (7x3 – 3x + 1) – (x3 + 4x2 – 2)

7. Multiplying by a Monomial
You can use the distributive property to multiply polynomials. Example 1: Multiply 3x and (2x + 1)

8. Multiply. a. 2x(4x – 3) b. (4x – 3)(2x)
Example 2
Multiply. a. 2x(4x – 3) b. (4x – 3)(2x)

9. Factoring out a monomial
Factoring a polynomial reverses the multiplication process. To factor out a monomial using the distributive property, it is helpful to find the greatest common factor (GCF).
Example 3: Find the GCF of the terms of the polynomial
4x3 + 12x2 – 8x

10. Find the GCF of the terms of each polynomial. 4x3 – 2x2 – 6x
Example 4
Find the GCF of the terms of each polynomial.
4x3 – 2x2 – 6x
5x5 + 10x3
3x2 – 18

11. Step 1: Find the GCF Step 2: Factor out the GCF
Example 5: Factor 3x3 – 9x2 + 15x
Step 1: Find the GCF Step 2: Factor out the GCF

12. Factor each polynomial. 8x2 – 12x 5x3 + 10x 6x3 – 12x2 – 24x
Example 6
Factor each polynomial.
8x2 – 12x
5x3 + 10x
6x3 – 12x2 – 24x

13. Complete take home quiz.
Homework
Complete take home quiz.