First Ten 8- 11 Simplify the following:1) 2) 3)

Determine if the following are irrational or rational4) + π5)5.2 – 6)7)

Polynomials

VocabularyDegree: The largest exponentStandard Form: Descending order according to exponentsLeading Coefficient: The number in front of the variable with the highest exponent (including sign)

# of Terms

Name by # of Terms

1 Monomial

2 Binomial

3 Trinomial4+ Polynomial

Degree

(largest exponent)

Name by degree

0 Constant

1 Linear

2 Quadratic

3 Cubic4

Quartic

Examples:Name the following by degree and number of terms.

1. 6x3 Degree Name:_____________ # of Terms

Name:_____________

2. 12x2 + 7x Degree Name:_____________ # of Terms

Name:_____________

3. 3x - 5 - 2x2 Standard Form:

Degree:

Name by Degree:

Leading Coefficient:

Name by # of Terms:

Adding Polynomials

Step 1: Group like terms together

* same variable * same exponent

Step 2: Simplify* Combine like terms

Examples4. (2x2 – 4x + 3) + (x2 + 5x – 1)

5. (6 + x2) + (2x – 8)

6. (5x - 3x2 + 1) + (-6 + x2 - 2x)

7. (2 - x2 + x) + (x2 - 2x + 4)

Subtracting Polynomials

Step 1: Distribute the subtraction sign to the ( ) after it.

Step 2: Group like terms

Step 3: Simplify * Combine like terms

Examples8. (3a2 + 10a) - (8a2 - a)

9. (7x - 3) - (9x – 2)

10. (3x2 + 2x - 4) - (2x2 + x - 1)

First Ten 8- 12 Simplify the following expressions then a) Write in Standard Formb) Classify by the number of termsc) State the leading coefficientd) State the degree

1) (7x3 + 6x2 – 2x) + (9x2 – 4x + 3)

2) (2x2 – 4x + 4) – (-2x2 – 5x + 4)

Multiplying Polynomials

Multiply the coefficients

Add the exponents

Examples (monomials)1. (5x2)(-2x3)

2. (2x2)(10x3 - 7x5)

3. (3x2)(3x3 – 7x + x2 + x5)

Binomial * BinomialStep 1: Every term from the first binomial needs to get distributed to EVERY term in the second binomialStep 2: Group like termsStep 3: Simplify to trinomial (sometimes binomial)

* Combine like terms

4. (x + 9)(x + 3)

5. (x+4)(x-7)

6. (3w-1)(2w-4)

7. (5b - 6)(3b2 – 2b + 5)Binomial * Trinomial

8. (b2 + 1)(2b2 + 4b - 11)

Last Ten 8- 12 1) How many centimeters are in 12 kilometers?

2) Simplify

3) Write a binomial with a degree of 2 and a leading coefficient of 3

First Ten 8 - 13 Simplify the following expression and write them in standard form

1) 2x4(-5x3 + 10x + 1)

2) (x + 2)(2x + 4)

3) (6x3 – 1)(2x + 5)

4) (x + 2)(x2 – 4x + 8)

Polynomials and PerimeterPerimeter: The length around the outside of a shape

1) A triangle is shown below. Write an expression for the perimeter of the triangle.

x2 + 6x - 4

x2 + 15

5x +2

2. A sandbox has a length that is 6 inches longer than its width. Draw a picture then write an expression that represents the perimeter.

Polynomials and AreaAREA: The space INSIDE of an object.

Common Area FormulasTriangle: A = ½bh Rectangle: A = lwCircle: C = 2πr

3. Write the expression for the area of the rectangle from problem #2

4. Write an expression for the area of the following shape

x + 6

2x - 4

Polynomials and VolumeVolume: The space INSIDE of a three dimensional object.

Cube/rectangular prismV = lwh

lw

h