Adding and subtracting Polynomials Lesson 8-1 TOPIC IX: Quadratic Equations and Functions

What does each prefix mean? mono one bi two tri three

Monomial is a real number, a variable, or a product of a real number and one or more variables with whole- number exponent. Here are some examples of monomials

What about poly? one or more A polynomial is a monomial or a sum/difference of monomials. Important Note!! An expression is not a polynomial if there is a variable in the denominator.

You can name a polynomial based on its degree or the number of monomials it contains

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x 3 yz 2 monomial 3) not a polynomial

Which polynomial is represented by X2X2 1 1 X X X 1.x 2 + x x 2 + x x 2 + 2x x 2 + 3x I’ve got no idea!

The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x 2 2 2)4a 4 b 3 c 8 3)-3 0

To find the degree of a polynomial, find the largest degree of the terms. 1) 8x 2 - 2x + 7 Degrees: Which is biggest? 2) y 7 + 6y 4 + 3x 4 m 4 Degrees: is the degree! 8 is the degree!

Find the degree of x 5 – x 3 y

A polynomial is normally put in ascending or descending order. What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents.

Means that the degrees of its monomial term decrease from left to right

Put in descending order: 1)8x - 3x 2 + x x 4 - 3x 2 + 8x - 4 2) Put in descending order in terms of x: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -6x 3 y x 2 y 3 - 2x + 3y

3) Put in ascending order in terms of y: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -2x + 3y - 6x 3 y x 2 y 3 4)Put in ascending order: 5a a - a a - a 2 + 5a 3

Write in ascending order in terms of y: x 4 – x 3 y 2 + 4xy – 2x 2 y 3 1.x 4 + 4xy – x 3 y 2 – 2x 2 y 3 2.– 2x 2 y 3 – x 3 y 2 + 4xy + x 4 3.x 4 – x 3 y 2 – 2x 2 y 3 + 4xy 4.4xy – 2x 2 y 3 – x 3 y 2 + x 4

You can add and subtract monomial by adding and subtracting like terms. Examples:

Degree of each monomial Degree of each monomial

You can add polynomials by adding like terms Line up like terms then add the coefficients Method 1 – Add vertically Method 2 – Add horizontally Group like terms then add the coefficients

Recall that subtraction means to add the opposite. So when you subtract a polynomial, change each of the term to its opposite. Then add the coefficients Line up like terms Method 1 – Subtract vertically Then add the opposite of each term in the polynomial being subtracted

Method 2 – Subtract horizontally Write the opposite of each term in the polynomial being subtracted Group like term Simplify

1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. (9y - 3y) + (- 7x + 8x) + (15a - 8a) = 6y + x + 7a Examples:

Combine your like terms. (3a 2 ) + (3ab + 4ab) + (6b 2 - b 2 ) 3a 2 + 7ab + 5b 2 2. Add the following polynomials: (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 )

Add the polynomials. + X2X2 11 X X XY Y Y Y Y 111 X Y Y Y x 2 + 3x + 7y + xy x 2 + 4y + 2x x + 7y x xy + 8

Line up your like terms. 4x 2 - 2xy + 3y 2 +-3x 2 - xy + 2y 2 _________________________ x 2 - 3xy + 5y 2 3. Add the following polynomials using column form (vertically): (4x 2 - 2xy + 3y 2 ) + (-3x 2 - xy + 2y 2 )

Rewrite subtraction as adding the opposite. 9y - 7x + 15a + 3y - 8x + 8a Group the like terms. 9y + 3y -7x - 8x + 8a +15a 12y - 15x + 23a 4. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)

Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b)

Line up your like terms and add the opposite 4x 2 - 2xy + 3y 2 + (+ 3x 2 + xy - 2y 2 ) 7x 2 - xy + y 2 6. Subtract the following polynomials using column form: (4x 2 - 2xy + 3y 2 ) - (-3x 2 - xy + 2y 2 )

Find the sum or difference. (5a – 3b) + (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 3b

Find the sum or difference. (5a – 3b) – (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 9b