1. ALGEBRA I - SECTION 8-1 (Adding and Subtracting Polynomials)
4/14/2019
ALGEBRA I @
SECTION 8-1 : ADDING and SUBTRACTING POLYNOMIALS

2. MONOMIAL : a number, a variable, or the product of a number and a variable.
Examples :
DEGREE of a MONOMIAL : is the sum of the exponents of the variables.
1) Find the degree of the monomial examples we just wrote.
BINOMIAL : the sum or difference of two monomials.
Examples :

3. TRINOMIAL : the sum and/or difference of three monomials.
Examples :
POLYNOMIAL : is a monomial or the sum or difference of monomials. A polynomial can have 1, 2, 3, or more terms.
Examples :
The degree of a polynomial is the largest degree of a monomial in the polynomial.
2) Find the degree of each polynomial we just wrote.

4. STANDARD FORM of a POLYNOMIAL : means the monomial’s degrees decrease from left to right.
Examples :
NAMES OF POLYNOMIAL
DEGREE
NAME
EXAMPLE
constant 1
linear 2
quadratic 3
cubic 4
quartic

5. Write each polynomial in Standard Form
Write each polynomial in Standard Form. Then, name the polynomial by its degree and number of terms.
3) 4x + 5x2
ANSWER : 5x2 + 4x, quadratic binomial
4) 4x + 1 – 5x2 + 7x
ANSWER : -5x2 + 11x + 1, quadratic trinomial
5) 3x2 + 2x – 1 + 7x3
ANSWER : 7x3 + 3x2 + 2x – 1, cubic trinomial

6. In order to add or subtract polynomials, you add/subtract like terms
In order to add or subtract polynomials, you add/subtract like terms. There are two ways to add or subtract polynomials – horizontally and vertically. We’ll try both methods.
6) (4x - 3) + (2x + 5)
ANSWER : 6x + 2
7) (x² + 2x - 5) + (3x² - x + 4)
ANSWER : 4x2 + x - 1

7. 8) 4x - 3 (Align all like terms) (+) 2x + 5
ANSWER : 6x + 2
9) a² - 2ab + 4b²
(+) 7a² b²
ANSWER : 8a2 – 2ab + 2b2

8. To subtract polynomials, distribute the negative and add like terms.
10) (6x + 5) - (3x + 1)
ANSWER : 3x + 4
11) (3x - 2) - (-4x + 2x² - 9)
ANSWER : -2x2 + 7x + 7

9. 12) 3x² + 5 (-) 2x² - 4x + 3 14) (5x² + 4x - 1) - (4x² + x + 2)
ANSWER : x2 + 3x - 3
ANSWER : x2 + 4x + 2
15) (2x² - 5x + 4) + (3x² - 1)
13) 6m² - 5m + 3
(-) 5m² + 2m - 7
ANSWER : 5x2 – 5x + 3
ANSWER : m2 – 7m + 10