Lesson 5.3 Operations with Polynomials

Combine Like Terms Warm up 5x – 14 15x2 + 3x 4xy – 9y 3x – 6 + 2x – 8 10xy + 5y – 6xy – 14y 5x – 14 15x2 + 3x 4xy – 9y

VOCABULARY

Polynomial Term Variable Coefficient Constant Degree of term Degree of polynomial Leading coefficient Standard form

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

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

Linear Binomial 9 Special Names: Degree Name: # of Terms Name: Constant: Binomial 9

Special Names: Degree Name: # of Terms Name: Cubic Monomial

Quadratic Binomial 4 Special Names: Degree Name: # of Terms Name: Leading Coefficient: Binomial 4

Cubic Trinomial 1 Special Names: Degree Name: # of Terms Name: Leading Coefficient: Trinomial 1

Adding Polynomials

1. 3x2 + x + 2

2. x2 + 2x – 2

Subtracting Polynomials

When SUBTRACTING polynomials Drop the 1st parenthesis then distribute the NEGATIVE to the 2nd parenthesis.

3. 3a2 + 10a – 8a2 + a – 5a2 + 11a

4. 3x2 + 2x – 4 – 2x2 – x + 1 x2 + x – 3

Multiplying Polynomials

5. -2x(x2 – 4x + 2)

6. (3x – 1)2 9x2 – 6x + 1

7. (x – 3)(x2 + 4x – 2) x3 + x2 -14x + 6

8. (x + 1)(x + 2)(x – 5) x3 – 2x2 – 13x - 10

9. Find the area of the rectangle.