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Unit 2: Polynomials 2017 PEBBLEBROOK HIGH SCHOOL ALGBRA 2 2.1 – 2.6
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Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

Jun 09, 2018

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Page 1: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

Unit 2: Polynomials

2017

pebblebrook high schoolALGBRA 2

2.1 – 2.6

Page 2: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

2.1 Classify PolynomialsVocabulary:

Page 3: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Page 4: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Page 5: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

You Try…..

2.2 Multiplying Polynomials

Method….Use area method (Box)

Page 6: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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.

Page 7: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Page 8: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Examples: Area & Perimeter.

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

Page 9: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

2) Find the volume of the rectangular prism.

You try…

Section 2.4 Binomial Theorem

Page 10: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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.

Page 11: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3
Page 12: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Page 13: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Page 14: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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)

Page 15: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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))

Page 16: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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

Page 17: Unit 2: Polynomials  · Web view2018-02-06 · 2.1 – 2.6. Unit 2: Polynomials. pebblebrook high school. Algbra 2. 2017. 2.1 – 2.6. ... Adding & Subtracting Polynomials ... 2.3

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)