Unit 2: Polynomials

2017

pebblebrook high schoolALGBRA 2

2.1 – 2.6

2.1 Classify PolynomialsVocabulary:

Polynomial Monomial or the sum of monomials

Degree of the term

The exponent of the variable

Standard form of a polynomial

The terms of the polynomial are written in descending order by the degree of the term.

Degree of the polynomial

The largest degree of any term of the polynomial.

Classify using the degree of the polynomial(First Name)

Degree Name using Degree0 Constant1 Linear2 Quadratic3 Cubic4 Quartic5 Quintic

Classify using the number of terms(Last Name)

Number of Term

Name using the number of terms

1 Monomial2 Binomial3 trinomial4 OR MORE Polynomial

Example #1: Classify the polynomial. Then write in standard form

Examples of Polynomials

Classify the polynomial

Standard form

63 + x3x2

3x2+ x4

-2x + 2x3+ 5x2

-x + 2x – 3x2 – 2x5+ 4

You Try….

Classify & Write the polynomial in standard form.

1) -7x + 5x4

2) x2- 4x + 3x2+ 2x

Adding & Subtracting Polynomials…You can only add & subtract like terms (CLT)

Example #2: Add or Subtract

You Try…..

2.2 Multiplying Polynomials

Method….Use area method (Box)

Examples: Multiply1) Multiply. Then classify the polynomial.

2) Multiply. Then classify the polynomial.

3) Multiply. Then classify the polynomial.

4) Multiply. Then classify the polynomial.

You Try….Multiply. Then classify the polynomial.

2.3 Word Problems: Area, Volume, & Perimeter.Area = lw Volume = lwh Perimeter = add lengths

Don’t forget about area formulas for the other shapes…

Examples: Area & Perimeter.

Examples: Volume1)Find the volume of the rectangular prism.

2) Find the volume of the rectangular prism.

You try…

Section 2.4 Binomial Theorem

Multiply (x + 1)8……

Yes, there is a short cut: The Binomial Theorem.

Before we understand the pattern, let’s talk about Pascal’s Triangle.

Pascal’s Triangle is a triangular array of numbers formed by first lining the border with 1’s and then placing the sum of the two adjacent numbers within a row between and underneath the 2 original numbers.

Expand (Multiply) (a + b)4

1st: Number the terms

2nd: Use the pattern to simplify the each term

3rd: Simplify

Examples: Expand

1) (x + 2)3

2) (x – 4)4

3) (v + w)9

4) (2x – 3)5

You try…

1) (x – 1)4 2) (g + h)6 3) (c – 2)5

Section 2.5 Function OperationsA function is a relation in which each element of the domain (x-values) is paired with exactly one element in the range (y-values).

Visuals help….Wet clothes → Dryer → Dry Clothes

Input → equation → output

x → f(x)→ y

Recall…If f(x) = x + 5, thenx f(x)

Example #1: Adding, Subtracting & Multiplying FunctionsLet f(x) = 3x + 8, g(x) = 2x -12 and h(x) = -4x

1) f + g =

2) f – g =

3) g – f =

4) g * f =

5) g * h =

6) h – f =

Composite functions

In other words…

f(x) → g(x) →(g ○ f)

Example #2: Composition of a FunctionLet f(x) = x – 2 and g(x) = x2.

1) f(f(-5))

2) g(f(0))

3) f(g(-2))

4) f(g(3))

You try… Let f(x) = 3x + 5 and g(x) = x2

1) f(x) + g(x)

2) f(x) * g(x)

3) f(g(x))

Section 2.6 Inverse Functions

In other words, the input and output switches places…

Example #1: Find the inverse from a table of points.

Example #2: Find the inverse from an equation.

Step 1: Switch x & yStep 2: solve for y.

1) y = x2 + 3

2) y = √ x+1

3) y = 2x + 6

To verify if 2 functions are inverses of one another, you must find the composition of f(g(x)) AND g(f(x)). THE BOTH MUST SIMPLIFY TO X!

Example #3: Verify the functions are inverses of one another.

1)

2)

3)