12/2/13 Challenge

1. 3x + 6x2 – 10 + 9x2 + 2x

2. 5x2y + 3xy – 8x2y + 6xy

3.

4. (2x2)(-4x3)

5. 2(x + 4)

6. 7(12 + 3x) – 102x + 8

-8x5

15x2 + 5x - 10

-3x2y + 9xy

21x + 74

36

2

x

x 3x2

Objective: To classify polynomials by degree and by number of terms

Classifying Polynomials

Example of a Polynomial

5364 23 xxx

Coefficients

Degrees

Constant

Vocabulary

Degree: is the exponent for each variable.

Degree of the polynomial: is the largest exponent of the polynomial.

Leading coefficient: is the coefficient of the first term.

Descending order/Standard form is how polynomials are written where the terms are placed in descending order from largest degree to smallest.

Example: Write the polynomials in Standard form/descending order. Then identify the leading coefficient and degree of the polynomial.

372 35 xxx 1. 237 53 xxx Degree is 7Leading coefficient is 3

2. 124 4 xx 142 4 xxDegree is 4leading coefficient is –2

Classifying Polynomials By Degree

Degree Example Example

Constant 0 6 -3

Linear 1 3x + 4 -7x + 2

Quadratic 2 123 2 xx 46 2 x

Cubic 3 325 23 xx xx 33

Quartic 4 23 34 xx xxx 24 85

Classifying polynomials By # of terms

# of terms Example Example

Monomial 1 3x 27x

Binomial 2 3x + 1 xx 28 3 Trinomial 3 523 26 xx 534 2 xx

Note: Any polynomials with four or more terms are just called polynomials

Adding and Subtracting Polynomials

Adding

• Drop the parentheses and combine like terms.

2 2 2 2a ab 3b 4a ab b

Practice

2 21) (3 7 4) (9 8 4)x x x x

2 22) (8 4 6) ( 4 10)x x x x

Subtracting

• Distribute the negative to all terms in the 2nd parenthesis. This will change all of the signs of each term. Then, combine like terms.

2 2 2 2a ab 3b 4a ab b

Practice2 21) (3 7 4) (9 8 4)x x x x

2 22) (8 4 6) ( 4 10)x x x x

Multiplying Polynomials

Monomial x Polynomial

(5)(x + 6)

5 30x

(x2)(x + 6)

3 26x x

(-2x)(x2 – 4x + 2)

3 22 8 4x x x

Multiplying Polynomials

Binomial x Binomial or Trinomial

Multiplying Polynomials

Using the distributive property

Multiplying Polynomials

F - First

O - Outside

I – Inside

L - Last

(z + 5) (z + 3)

(x - 2) (x + 4)

2 2 8x x

(x + 9) (x – 3)

2 6 27 x x

(x + 3) (x – 3)

2 27x

(2x + 5)(x + 6)

22 17 30 x x

(3x – 1)(2x – 4)

26 14 4 x x

(5b – 6)(3b2 – 2b + 5)This is NOT FOIL!

3 215 28 37 30 b b b

Find the area of the rectangle.

228 96 80 x x

7 10x

4 8x

Find the area of the rectangle.

25 21 4 x x

4x

5 1x

Find the volume.

3 29 18 x x x

3x

6x

x

Practice Worksheet