First Ten 8- 11. Degree: The largest exponent Standard Form: Descending order according to exponents Leading Coefficient: The number in front of the.

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Presentation transcript:

First Ten 8- 11

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)

# of Terms Name by # of Terms 1 Monomial 2 Binomial 3 Trinomial 4+Polynomial

Degree (largest exponent) Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic

Examples: Name the following by degree and number of terms. 1. 6x 3 Degree Name:_____________ # of Terms Name:_____________ 2. 12x 2 + 7x Degree Name:_____________ # of Terms Name:_____________

3. 3x x 2 Standard Form: Degree: Name by Degree: Leading Coefficient: Name by # of Terms:

Step 1: Group like terms together * same variable * same exponent Step 2: Simplify * Combine like terms

Examples 4. (2x 2 – 4x + 3) + (x 2 + 5x – 1) 5. (6 + x 2 ) + (2x – 8) 6. (5x - 3x 2 + 1) + (-6 + x 2 - 2x) 7. (2 - x 2 + x) + (x 2 - 2x + 4)

Step 1: Distribute the subtraction sign to the ( ) after it. Step 2: Group like terms Step 3: Simplify * Combine like terms

Examples 8. (3a a) - (8a 2 - a) 9. (7x - 3) - (9x – 2) 10. (3x 2 + 2x - 4) - (2x 2 + x - 1)

First Ten Simplify the following expressions then a)Write in Standard Form b)Classify by the number of terms c)State the leading coefficient d)State the degree 1)(7x 3 + 6x2 – 2x) + (9x 2 – 4x + 3) 2)(2x 2 – 4x + 4) – (-2x 2 – 5x + 4)

Multiply the coefficients Add the exponents

Examples (monomials) 1. (5x 2 )(-2x 3 ) 2. (2x 2 )(10x 3 - 7x 5 ) 3. (3x 2 )(3x 3 – 7x + x 2 + x 5 )

Step 1: Every term from the first binomial needs to get distributed to EVERY term in the second binomial Step 2: Group like terms Step 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)(3b 2 – 2b + 5)

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

Last Ten 8- 12

First Ten Simplify the following expression and write them in standard form 1)2x 4 (-5x x + 1) 2)(x + 2)(2x + 4) 3)(6x 3 – 1)(2x + 5) 4)(x + 2)(x 2 – 4x + 8)

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

1) A triangle is shown below. Write an expression for the perimeter of the triangle. x 2 + 6x - 4 x x +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 Area AREA: The space INSIDE of an object. Common Area Formulas Triangle: A = ½bh Rectangle: A = lw Circle: 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 Volume Volume: The space INSIDE of a three dimensional object. Cube/rectangular prism V = lwh l w h