Bell work 8-21-12

2330 342 xyyxyx

2222 xyx

3

34

2

3

xy

yx)323(4)432(3 22 xyxxyx

)142(3)473( baba

Simplify

Simplify

ObjectivesThe student will be able to:

1. find the degree of a polynomial.

2. arrange the terms of a polynomial in ascending or descending order.

SOL: noneDesigned by Skip Tyler, Varina High School

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 polynomial2

57

2y

y

The degree of a monomial is the sum of the exponents of the variables.

Find the degree of each monomial.1) 5x2

2

2) 4a4b3c

8

3) -3

0

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

1. 0

2. 2

3. 3

4. 5

5. 10

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.

Put in descending order:

1) 8x - 3x2 + x4 - 4

x4 - 3x2 + 8x - 4

2) Put in descending order in terms of x:

12x2y3 - 6x3y2 + 3y - 2x

-6x3y2 + 12x2y3 - 2x + 3y

3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x

-2x + 3y - 6x3y2 + 12x2y3

4) Put in ascending order:5a3 - 3 + 2a - a2

-3 + 2a - a2 + 5a3

Write in ascending order in terms of y:x4 – x3y2 + 4xy – 2x2y3

1. x4 + 4xy – x3y2– 2x2y3

2. – 2x2y3 – x3y2 + 4xy + x4

3. x4 – x3y2– 2x2y3 + 4xy

4. 4xy – 2x2y3 – x3y2 + x4

ObjectivesThe student will be able to:

1. add and subtract polynomials.

SOL: A.11

Designed by Skip Tyler, Varina High School

1. Add the following polynomials:(9y - 7x + 15a) + (-3y + 8x - 8a)

Group your like terms.

9y - 3y - 7x + 8x + 15a - 8a

6y + x + 7a

Combine your like terms.

3a2 + 3ab + 4ab - b2 + 6b2

3a2 + 7ab + 5b2

2. Add the following polynomials:(3a2 + 3ab - b2) + (4ab + 6b2)

Line up your like terms. 4x2 - 2xy + 3y2

+ -3x2 - xy + 2y2

_________________________

x2 - 3xy + 5y2

3. Add the following polynomials using column form:

(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)

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

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 - 4b4a - 14b

5. Subtract the following polynomials:(7a - 10b) - (3a + 4b)

Line up your like terms and add the opposite.

4x2 - 2xy + 3y2

+ (+ 3x2 + xy - 2y2)--------------------------------------

7x2 - xy + y2

6. Subtract the following polynomials using column form:

(4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)

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

yx 43

yx 5

The measures of two sides of a triangle are given. If P is the perimeter, and , find the measure of the

third side. yxP 510