Homework Log

Wed

12/9

Lesson Rev

Learning Objective: To remember everything about Polynomials!

Hw: Quiz Corrections

Homework Log

Wed

12/9

Lesson Rev

Learning Objective: To remember everything about Polynomials!

Hw: Test Review WS

12/9/15 Chapter 5 Review

Algebra II

To remember everything about Chapter 5

Learning Objective

1. Quintic Binomial

Write in standard form & classify by degrees & number of terms.

2. What is a cubic polynomial function in standard form with zeros –2, , and 0?x = –2 x = x = 0x + 2 = 0 3x = 4 x = 0x + 2 = 0 3x - 4 =0 x = 0(x + 2)(3x – 4)(x) = 0 (

Write a Polynomial Function From its Zeros

3. Write a polynomial function with rational coefficients so that

P(x) = 0 has the given roots of and

must also be a root!x = x = x = x + 3 = 0 x – = 0 x + = 0

(x + 3)(x - )(x + ) = 0

Write a Polynomial Function From its Roots

(x + 3)(x - )(x + ) = 0

- x

–x 𝑥2

-49x

x

7 𝑖

3 x

3 𝑥3

14749x

49

-49 = 49

4. Write a polynomial function with rational coefficients so that

P(x) = 0 has the given roots of

must also be a root!x = x = x=0 x=0

(x)(x) = 0

Write a Polynomial Function From its Roots

(x)(x) = 0

-3x𝑥2

9-3x

x

-3

-3𝑥 2√5

−6 √5 6 √5−4 √25

= 0

= -20

5. (2x – 3)(42x – 3 = 0 4x =

Find all the roots

2x 3

6. Divide by Long Division

4 𝑥−1 8 𝑥3+18 𝑥2+7 𝑥−32 𝑥2

8 𝑥3 -

12x

+5x

20 +7x-

20 -5x

-

--

-312x - 3-

-

0R

+ 3

7.

Divide using Synthetic Division

=

x = 1

1𝑥2 𝑥¿00 −15

1

1

11−14

𝑥¿ 𝑅

𝑥3

1

1𝑥2

1

8. , what is ?Remainder Theorem

-2𝑥3𝑥2 𝑥¿1−5 0 7

17−34−397878

−156−149

3

3−6

𝑅

𝑥4

−2

−8

𝑥5

16

-149

9. Is a factor of ? If it is, find the remaining factors.

Factor Theorem

2𝑥3 𝑥2 𝑥¿10 −1216

1

2

24−8−16

0𝑥2 𝑥¿ 𝑅

R 0, so x - 2 is a factor of P(x)!

+ 2x - 8 Factor more!

9. =

= (x - 2)(x - 2)(x + 4) =

Factor Theorem

10. What are the rational roots of

Applying Rational Root Theorem

, ,

Step 2: Test each possible rational root in original function until you find a root.

Do synthetic substitution until get R0

10.

Applying Rational Root Theorem

1𝑥3 𝑥2 𝑥 ¿11 −17 15

1122−15

−150 YES! 1 IS a

root!Factor & Solve to find rest of the roots!(x – 3)(x + 5)

x = 1, –5, 3

𝑥2 𝑥¿ 𝑅

11. Find all Roots

1𝑥3 𝑥2 𝑥 ¿1 −1 4 −4

1100440 YES! 1 IS a root!

is not factorable, so the only RATIONAL ROOT is 1

*Can solve = 0 to find imaginary roots

𝑥2 𝑥¿ 𝑅

x =1,

,

12.

Descartes’ Rule of Signs

3 Sign Change

2 Sign Change

12. , so should have 5 solutions totalDescartes’ Rule of Signs

+ -

3 2 03 0 21 2 21 0 4

13. What are ALL the roots of

Applying FTA

q = 1 p = 24

=

= 2, 3, 4, 6, 8, 12, 24

13.Applying FTA

2𝑥3 𝑥2 𝑥¿1 −2 4 −24

364812240

𝑥2 𝑥¿ 𝑅

𝑥41

1𝑥3

2

-313 4 12

1−3004

−120

𝑥2 𝑥¿ 𝑅

13.

x =

Applying FTA

Assignment:

Chapter 5 Test Review WS