1. Polynomial Review / Adding, Subtracting, and Multiplying Polynomials

2. Polynomials
A monomial is an expression that consists of a numeral, a variable, or the product of a numeral and one or more variables.
A number can also be called a constant.
A sum of monomials is called a polynomial.
A polynomial that has 2 terms is called a binomial.
A polynomial that has 3 terms is called a trinomial.

3. Polynomials Recap : one term ----monomial two terms ---binomial
three terms –trinomial
more than 3 ---polynomial
Okay …time for “Name the ‘nomial”…..

4. Coefficients
The number preceding or in front of a variable is called the coefficient.
In the monomial , the numeral -3 is the coefficient.
Name the coefficient…

5. Putting polynomials in descending powers of the variable.
When writing answers you should always put the terms in descending (greatest to smallest) order. This is called Standard Form. For example: Should be written as:

6. Like Terms Which terms are like? 3a2b, 4ab2, 3ab, -5ab2
Like Terms refers to monomials that have the same variable(s) raised to the same power, but may have different coefficients.
Which terms are like? a2b, 4ab2, 3ab, -5ab2
4ab2 and -5ab2 are like.
Even though the others have the same variables, the exponents are not the same.
3a2b = 3aab, which is different from 4ab2 = 4abb.

7. Constants are like terms.
Which terms are like? x, -3, 5b, 0
-3 and 0 are like.
Which terms are like? x, 2x2, 4, x
3x and x are like.
Which terms are like? wx, w, 3x, 4xw
2wx and 4xw are like.

8. Adding Polynomials (x2 + 3x + 1) + (4x2 +5)
Add: (x2 + 3x + 1) + (4x2 +5)
Step 1: Identify like terms:
(x2 + 3x + 1) + (4x2 +5)
Notice: ‘3x’ doesn’t have a like term.
Step 2: Add the coefficients of like terms, do not change the powers of the variables. Make sure you write the answer in descending powers.
(x2 + 4x2) + 3x + (1 + 5)
5x2 + 3x + 6

9. Adding Polynomials

10. Subtracting Polynomials
Subtract: (3x2 + 2x + 7) - (x2 + x + 4)
Step 1: Write the first polynomial exactly the way it is written. Then rewrite the second polynomial by distributing the negative sign through the entire polynomial.
3x2 + 2x x2 - x - 4
Step 2: Combine like terms
2x x + 3

11. Subtracting Polynomials
Remember to rewrite the polynomials!!!!!!

12. Multiplying Polynomials
Monomial x Polynomial (Distribute)
5𝑥( 3𝑥 4 +3x−1)
Binomial x Binomial (Foil)
(2𝑥+1)( 3𝑥 2 +2)
Polynomial x Polynomial (Distribute or use “the box”)
( 2𝑥 2 −5x−4)( 𝑥 2 +x−2)