1. Adding and Subtracting Polynomials
Ch 8-1
Students will be able to classify, add, and subtract polynomials.
Adding and Subtracting Polynomials
Algebra 1 Foundations, pg 502

2. Ch 8-1
Students will be able to classify, add, and subtract polynomials.
In some cases, you can model a situation with an expression composed of monomials. A monomial is a real number, a variable, or a product of a real number and one or more variables with whole-number exponents. Here are some examples of monomials.
18 z -4x xy3 a3
Focus Question
How are monomials and polynomials related?
Polynomials are formed by adding and subtracting monomials. You can add and subtract two polynomials by combining like terms.
Algebra 1 Foundations, pg 502

3. Ch 8-1
Students will be able to classify, add, and subtract polynomials.
The degree of a monomial is the sum of the exponents of its variables. The degree of a nonzero constant is 0. Zero has no degree.
What is the degree of each monomial?
5x Degree: ___
6x3y2 Degree: ___
4 Degree: ___
8xy Degree: ___
-7y4z Degree: ___
11 Degree: ___
Problem 1 1 5 2
Algebra 1 Foundations, pg 502

4. Ch 8-1 You can add or subtract by adding or subtracting like terms.
Students will be able to classify, add, and subtract polynomials.
You can add or subtract by adding or subtracting like terms.
Problem 2
What is the sum or difference?
3x2 + 5x x3y – x3y
3. -6x4 + 11x x2y4 – 7x2y4
8x x3y
5x4 – 5x2y4
Algebra 1 Foundations, pg 503

5. Degree of each monomial
Students will be able to classify, add, and subtract polynomials.
A polynomial is a monomial or sum of monomials. The following polynomial is the sum of the monomials 3x4, 5x2, x, and 1.
The polynomial shown above is in standard form. Standard form of a polynomial means that the degrees of its monomial terms decrease from left to right. The degree of a polynomial in one variable is the same as the degree of the monomial with the greatest exponent. The degree of 3x4 + 5x2 – 7x + 1 is 4.
3x4 + 5x2 - 7x + 1
Degree of each monomial
Algebra 1 Foundations, pg 503

6. Name Using Number of Terms
Ch 8-1
Students will be able to classify, add, and subtract polynomials.
You can name a polynomial based on its degree or the number of monomials it contains.
Polynomial
Degree
Name Using Degree
Number of Terms
Name Using Number of Terms 6
5x + 9
4x2 + 7x + 3
2x3
8x4 – 2x3 + 3x
constant monomial
linear binomial
quadratic trinomial
cubic monomial
th degree trinomial
Algebra 1 Foundations, pg 503

7. Ch 8-1
Students will be able to classify, add, and subtract polynomials.
Problem 3
Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms?
3x + 4x x – 1 + 5x2 + 7x
3. 2x – 3 + 8x3
4x3 + 3x x2 + 4x + 7x – 1
Degree is 3 and 2 terms Degree is 2 and 3 terms
Cubic binomial Quadratic trinomial
8x3 + 2x – 3
Degree is 3 and 3 terms
Cubic trinomial
Algebra 1 Foundations, pg 503

8. Ch 8-1 You can add polynomials by adding like terms. Problem 4
Students will be able to classify, add, and subtract polynomials.
You can add polynomials by adding like terms.
Problem 4
Adding polynomials.
Algebra 1 Foundations, pg 504

9. Ch 8-1
Students will be able to classify, add, and subtract polynomials.
Recall that subtraction means to add the opposite. So when you subtract a polynomial, change each of the terms to its opposite. Then add the coefficients.
Problem 5
Subtracting polynomials.
Algebra 1 Foundations, pg 505