Unit 4 Solving Polynomials: Pre-Unit

Guided Notes

_________________________________________________Name

______________Period

**If found, please return to Mrs. Brandley’s room, M-8.**

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Self-AssessmentThe following are the concepts you should know by the end of Unit 1. Periodically throughout the unit I will ask you to self-assess on how you are doing on these skills. It is essential for you to be able to identify what you do and do not understand in order to learn effectively. You will use the following scale:

5: Yes! I understand4: I’m almost there.3: I am back and forth.2: I am just starting to understand.1: I don’t understand at all.

Concept 1: Fundamental Theorem of Algebra

_____ I can tell how many solutions a polynomial has given the expression.

_____ I can tell how many real solutions, imaginary solutions, and total solutions a function has given its’

graph.

Concept 2: Complex Operations

_____ I know that i2=−1.

_____ I can add complex numbers.

_____ I can subtract complex numbers.

_____ I can multiply complex numbers.

Concept 3: Solving Radical Equations

_____ I can solve a radical equation with one solution.

_____ I can solve a radical equation with two solutions.

_____ I know what an extraneous solution is.

_____ I can identify extraneous solutions.

Concept 4: Finding Polynomials from their Solutions

_____ I can write a polynomial given the solutions to that polynomial.

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Concept 1: Fundamental Theorem of Algebra

Fundamental Theorem of Algebra: Any polynomial of degree n has n roots……but we may need to

use imaginary.

1. f ( x )=3 x+2 2. f ( x )=x2−4 3. f ( x )=x3+4 x2−6

Repeated Roots Exception

4. f ( x )=x2 5. f ( x )= (x−4 )2 6. f ( x )= (x−2 )3

Imaginary Roots Exception

7. f ( x )=x2+6 8. f ( x )=−x3+2 x2−2

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How many solutions do the following polynomials have?

How many solutions do the following functions have?

How many are complex and how many are real?

Concept 2

Complex Operations

REMINDER: √−1=¿ i2=¿

Adding, Subtracting, and Multiplying Polynomials Review:

(3 x2−3 x+2 )+(2 x2+5 x−7) (3 x2−3 x+2 )−(2x2+5 x−7) (x−5)(3 x2+4)

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Order of Operations Review:

P

E

MD

AS

Adding Complex Numbers:

Subtracting Complex Numbers:

Multiplying Complex Numbers:

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Let’s combine….

Concept 3: Solving Radical EquationsFactoring Review:

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1. x2+4 x+3=0 2. x2−13 x+42=0 3. x2−5 x+6=0

Solving Radical Equations:

1. 2=√4a 2. √1−16 x=7 3. √64−n=√ n7

4. √−2−x=√−7−2 x 5. p−2=√4 p−11 6. 6+3w=√2w+12+2w

Concept 4: Finding Polynomials from their SolutionsDetermine what x equals in the following equations.

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1. ( x−5 ) ( x+2 )=0 2. 3 (2x−1 ) (5 x+10 )=0 3. x (x−5 ) (3 x−6 ) (2 x+3 )=0

Find a polynomial that has the given solutions1. 5, 2 2. -2, 0, 4 3. ½, -2

4. 5/4, 0, -3 5. 3. 0, 5, 2, -3/2

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