Degree The largest exponent

Standard Form Descending order according to exponents

Leading Coefficient Once in standard form… The leading coefficient is the NUMBER out front (including its 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

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

Special Names: Quadratic Binomial Degree Name: # of Terms Name:

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

Adding Polynomials

Step 1: Group Like Terms Step 2: Simplify

1. 3x 2 + x + 2

2. x 2 + 2x – 2

3. -2x 2 + 3x – 5

4. -x + 6

Subtracting Polynomials

Step 2: Group Like Terms Step 3: Simplify Step 1: Distribute the subtraction sign

3a a – 8a 2 + a – 5a a

7x – 3 – 9x + 2 – 2x – 1

3x 2 + 2x – 4 – 2x 2 – x + 1 x 2 + x – 3

Multiplying Polynomials

Step 1: Multiply the Coefficients Step 2: Add the Exponents *If necessary, distribute!* Ex: (5x 2 )(-2x 3 )Ex: (5x 2 )(-2x 3 )

(5x 2 )(-2x 3 )

(2x 2 )(10x 3 -7x 5 )

(3x 2 )(3x 3 -7x + x 2 + x 5 )

Binomial * Binomial “FOIL” F O I L & Simplify

(x+9)(x+3) F O I L Simplified:

(x+4)(x-7) F O I L Simplified:

(3w-1)(2w-4) F O I L Simplified:

Binomial * Trinomial Step 1: Distribute First term in the binomial to all three terms in trinomial. Step 2: Distribute Second term in the binomial to all three terms in trinomial. Step 3: Simplify

(5b-6)(3b 2 – 2b + 5)

Dividing Polynomials by a Monomial

Step 1: Simplify the coefficients Step 2: Subtract the exponents