Combine Like Terms 1) 3x – 6 + 2x – 8 2) 3x – 7 + 12x + 10 Exponent Rules 3) What is 2x  3x? 5x – 14 15x + 3 6x 2 Warm up.

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Presentation transcript:

Combine Like Terms 1) 3x – 6 + 2x – 8 2) 3x – x + 10 Exponent Rules 3) What is 2x  3x? 5x – 14 15x + 3 6x 2 Warm up

Unit 1 Operations & Rules

Polynomial An expression that can have constants, variables, & exponents, but: No division by a variable Only whole number exponents  Named by their degree  Named by their number of terms  Written in standard form 5x 2 y – 3x y 3 – 9

Degree of the Polynomial Highest (largest) exponent of the polynomial

Standard Form Terms are placed in descending order by the DEGREE. Answers will always be written in this form.

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

1. What is the degree name? Linear

2. What is the degree name? Cubic

Adding Polynomials Drop the parenthesis & combine like terms

3. 3x 2 + x + 2

4. x 2 + 2x – 2

5. Find the perimeter of the rectangle. 10x + 12

Subtracting Polynomials Distribute the negative & combine like terms

3a a – 8a 2 + a – 5a a 6.

3x 2 + 2x – 4 – 2x 2 – x + 1 x 2 + x – 3 7.

Multiplying Polynomials Distribute, follow exponent rules, & combine like terms

-2x(x 2 – 4x + 2) 8.

(x + 3) (x – 3) 9.

(3x – 1)(2x – 4) 10.

11. Find the area of the rectangle.

12. Find the volume.

13. Profit Problem The Profit, P(x) for a diving company is represented by the product of the revenue per dive, R(x), and the number of customers, C(x). If R(x) = x and C(x) = 30 – 2x, find a polynomial representing P(x).

Homework Practice Worksheet