Objectives 1. find the degree of a polynomial.

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Presentation transcript:

Objectives 1. find the degree of a polynomial. arrange the terms in standard form Adding and subtracting polynomials

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

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.

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial

Which polynomial is represented by X 1 X 1 X2 X x2 + x + 1 x2 + x + 2 x2 + 2x + 2 x2 + 3x + 2 I’ve got no idea!

The degree of a monomial is the sum of the exponents of the variables The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x2 2 4a4b3c 8 -3

To find the degree of a polynomial, find the largest degree of the terms. 1) 8x2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2 is the degree! 2) y7 + 6y4 + 3x4m4 Degrees: 7 4 8 8 is the degree!

Find the degree of x5 – x3y2 + 4 2 3 5 10

What is descending order? Going from big to small exponents. A polynomial is normally put in ascending or descending order. This is called the STANDARD FORM OF A POLYNOMIAL. What is descending order? Going from big to small exponents.

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

2. Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2) Combine your like terms. 3a2 + 3ab + 4ab - b2 + 6b2 3a2 + 7ab + 5b2

Add the polynomials. + Y X X2 Y X XY Y X Y 1 1 Y 1 1 1 Y 1 1 1 Y x2 + 3x + 7y + xy + 8 x2 + 4y + 2x + 3 3x + 7y + 8 x2 + 11xy + 8

3. Add the following polynomials using column form: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Line up your like terms. 4x2 - 2xy + 3y2 + -3x2 - xy + 2y2 _________________________ x2 - 3xy + 5y2

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

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

6. Subtract the following polynomials using column form: (4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2) Line up your like terms and add the opposite. 4x2 - 2xy + 3y2 + (+ 3x2 + xy - 2y2) -------------------------------------- 7x2 - xy + y2

Find the sum or difference. (5a – 3b) + (2a + 6b)

Find the sum or difference. (5a – 3b) – (2a + 6b)