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Degree: The largest exponent Standard Form: Descending order according to exponents Leading Coefficient: The number in front of the variable with the highest exponent (including sign)
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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
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