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Remainder & Factor

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Finding Rational

Roots100 100 100

200 200 200

300 300 300

400 400 400

500 500 500

Is x+1 a factor of x15-3x-2

Yes

Accord. To Descartes Rule, what is the

possible # of positive roots of x3-2x2-5=0

1 Possible

List the possible rational roots of

4x4+3x2-1=0

± 1 , ± 2, ± 1/4

Find a poly. Whose roots are 0 and -1 d.r.

X3+2x2+x

Accord. To Descartes Rule, what is the

possible # of negative roots of x3-2x2-5=0

0 Negative

Solve over the real #’s x3-7x-6=0

(-1, -2, 3)

Solve 2y3-5y2-4y+3 with root 3

3,-1,1/2

Find a cubric eq. w/ R coffs. That has the roots

-1, 3-I

X3-5x2+4x+10=0

Solve over the complex #’s 4x4-4x3+5x2-

4x+1=0

1/2 (d.r.), ± i

Solve x4-x3-2x-4=0 with root

(±i, , -1, 2/3)

Find the remaining roots of x4+x3+6x2-14x-

20=0

-1 -3i ,-1

Solve over the Real #’s 2x3+x2-6x-3-x4+2x3-

2x2+18=0

Solve 3x4-5x3-7x2+3x+2=0

(1± , -1, 2/3)

Solve x4+12x-5=0

(1±2i, -1 ±

Solve over the complex #’s 6x4+x3+23x2+4x-

4=0

1/3, -1/2, ± 2i

Finding Rational

Roots

Answer page

Reminder and Factor

Thrm.

More Thrms. And

Rules.

2i

72

2 2

3,2

1

Is x+1 a factor of x15 - 3x – 2 ?

C1 – 100

Topic 1 – 100 / AnswerTopic 1 – 100 / Answer

Correct Question

C1-100 Q

Topic 1- 100 / QuestionTopic 1- 100 / Question

What is yes

Find a polynomial

whose roots are 0 and -1 double

root

C1 - 200

Topic 1 – 200 / AnswerTopic 1 – 200 / Answer

Correct Question

x3 + 2x2 + x

C1-200 Q

What is

Topic 1- 200 / QuestionTopic 1- 200 / Question

Solve

2y3 – 5y2 – 4y + 3

with root 3

C1 - 300

Topic 1 – 300 / AnswerTopic 1 – 300 / Answer

Correct Question

C1-300 Q

What is 3,-1, ½

Topic 1- 300 / QuestionTopic 1- 300 / Question

Solve

x4 – x3 – 2x – 4 = 0

with root

C1 - 400

Topic 1 – 400 / AnswerTopic 1 – 400 / Answer

Correct Question

2i

C1-400 Q

What are -1,2,

Topic 1- 400 / QuestionTopic 1- 400 / Question

2i

Solve

3x4–5x3–7x2+3x+2=0

given root

C1 - 500

Topic 1 – 500 / AnswerTopic 1 – 500 / Answer

Correct Question

21

C1-500 Q

What are , -1, 2/3

Topic 1- 500 / QuestionTopic 1- 500 / Question

21

According to Descartes’ Rule, what is the possible # of positive roots of

x3-2x2-5=0

C2 - 100

Topic 2 – 100 / AnswerTopic 2 – 100 / Answer

Correct Question

C2-100 Q

What is 1 positive

Topic 2- 100 / QuestionTopic 2- 100 / Question

According to Descartes’ Rule, what is the possible # of negative roots of

x3-2x2-5=0

C2 - 200

Topic 2 – 200 / Topic 2 – 200 / AnswerAnswer

Correct Question

C2-200 Q

What is 0 negative roots

Topic 2- 200 / QuestionTopic 2- 200 / Question

Find a cubic equation with real coefficients that has the roots -1 and 3-i.

C2 – 300

Topic 2 – 300 / AnswerTopic 2 – 300 / Answer

Correct Question

C2-300 Q

What is x3-5x2+4x+10=0

Topic 2- 300 / QuestionTopic 2- 300 / Question

Find the remaining roots of

x4+x3+6x2-14x-20=0 given its roots

2 and -1+3i

C2 - 400

Topic 2 – 400 / AnswerTopic 2 – 400 / AnswerCorrect Question

C2-400 Q

What are -1-3i and -1

Topic 2- 400 / QuestionTopic 2- 400 / Question

Solve x4+12x-5=0 given 1-2i is a root.

C2 - 500

Topic 2 – 500 / AnswerTopic 2 – 500 / Answer

Correct Question

C2-500 Q

What are

Topic 2- 500 / QuestionTopic 2- 500 / Question

2121 ,i

List the possible rational roots of 4x4 + 3x2 – 1 = 0

C3 - 100

Topic 3 – 100 / AnswerTopic 3 – 100 / Answer

Correct Question

C3-100 Q

What is

Topic 3- 100 / QuestionTopic 3- 100 / Question

4

1

2

11 ,,

Solve over the Real numbers:

x3 – 7x – 6 = 0

C3 - 200

Topic 3 – 200 / AnswerTopic 3 – 200 / Answer

Correct Question

C3-200Q

Topic 3- 200 / QuestionTopic 3- 200 / Question

What are-1,-2,3

C3 - 300

Topic 3 – 300 / AnswerTopic 3 – 300 / AnswerCorrect Question

Solve over the complex numbers:

4x4-4x3+5x2-4x+1=0

What are ½ d.r., i,-i

C3-300Q

Topic 3- 300 / QuestionTopic 3- 300 / Question

Solve over the

complex numbers:

2x3 + x2 - 6x – 3 =0

C3 - 400

Topic 3 – 400 / AnswerTopic 3 – 400 / Answer

Correct Question

C3-400Q

Topic 3- 400 / QuestionTopic 3- 400 / Question

What are

-1/2, 3

C3 - 500

Topic 3 – 500 / AnswerTopic 3 – 500 / Answer

Correct Question

Solve over the complex numbers:

6x4+x3+23x2+4x-4=0

C3-500Q

Topic 3- 500 / QuestionTopic 3- 500 / Question

What is

2

12

3

1 ,, i

POD