Add or subtract

1. (x2 + 4x – 1) + (5x2 – 6x + 4)

2. (5y2 – 9y + 1) – (7y2 – 8y – 6)

Find the product

3. (x – 6)(3x + 4)

4. (2x + 5)(3x + 4)

6x2 – 2x + 3

-2y2 – y + 7

3x2 – 14x – 24

6x2 + 23x + 20

# 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

74 2z

Identify the polynomial by degree and by the number

of terms.

LinearBinomial

Degree:

# of Terms:

Leading Coefficient:74

876 3r

Identify the polynomial by degree and by the number

of terms.

CubicMonomial

Degree:

# of Terms:

25 7 2x x

Identify the polynomial by degree and by the number

of terms.

QuadraticTrinomial

Degree:

# of Terms:

Leading Coefficient:5

Multiplying Polynomials

Binomial Theoremand

Pascal’s Triangle

Pascal’s Triangle

1 n = 0

1 1 n = 1

1 2 1 n = 2

1 3 3 1 n = 3

??? n = 4

Binomial Theorem 1 n = 0

1 1 n = 1

1 2 1 n = 2

1 3 3 1 n = 3(a+b)0 = 1

(a+b)1 = 1a + 1b

(a+b)2 = 1a2 + 2ab + 1b2

(a+b)3 = 1a3 + 3a2b + 3ab2

+ 1b3

Binomial Theorem 1 n = 0

1 1 n = 1

1 2 1 n = 2

1 3 3 1 n = 3

Use the binomial theorem to write out (x + 3)2.

Binomial Theorem 1 n = 0

1 1 n = 1

1 2 1 n = 2

1 3 3 1 n = 3

Use the binomial theorem to write out (x + 3)3.

Binomial Theorem 1 n = 0

1 1 n = 1

1 2 1 n = 2

1 3 3 1 n = 3

Try (x + 2)4.

Application

x + 2

x + 2

Find an expression for the area of the base and then, the volume of the box:

A = x2 + 4x + 4

V = x3 + 6x2 + 12x + 8

x + 2