Question 1

Using the remainder theorem, find the remainder when 4x³- 3x + 2x - 4 is divided by x - 1. (show your solution with synthetic division).

Accepted Answer

-13

Answer

30

Answer

13

Answer

-30

Question 2

Use the Remainder Theorem, find the remainder when x⁴ - 3x² + 4x - 12 is divided by x - 3. (show your solution with long division method).

Accepted Answer

54

Answer

27

Answer

-27

Answer

-54

Question 3

What number should be added to x² + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?

Accepted Answer

-11

Answer

6

Answer

-6

Answer

11

Question 4

What number should be subtracted from 3x² + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?

Accepted Answer

21/4

Answer

-18/4

Answer

-21/4

Answer

18/4

Question 5

Use the Remainder Theorem, find the remainder when 4x³ - 3x² + 2x - 4 is divided by x + 1. Type your answer.

Accepted Answer

-13

Question 6

Use the Remainder Theorem, find the remainder when x⁶ + 3x² + 10 is divided by x - 2. Type your answer.

Accepted Answer

86

Question 7

Is (x + 2) is a factor of x³ - 4x² - 2x + 20?

Accepted Answer

true

Answer

false

Question 8

Is (3x - 2) a factor of 3x³ + x² - 20x + 12?

Accepted Answer

true

Answer

false

Question 9

In f(x) = x³ - 3x + 1, (2 - 3x) is one of the factor.

Accepted Answer

false

Answer

true

Question 10

Find the value of m, if (x - 2) is a factor of the polynomial.

The value of m = - 2

Accepted Answer

false

Answer

true

Question 11

The following are the factors of f (x) = x³ + x² − 22x − 40 given 5 is the one zero, except;

Accepted Answer

x + 8

Answer

x + 4

Answer

x + 2

Answer

x - 5

Question 12

The following are the factors of f (x) = x³ + 11x² + 38x + 40, given - 2 is the one zero, except;

Accepted Answer

x + 1

Answer

x + 5

Answer

x + 2

Answer

x + 4

Question 13

How many possible number of positive and negative zeroes have f (x) = 3x⁴ + 20x² − 32.

Accepted Answer

Positive = 1

Negative = 1

Answer

Positive = 1

Negative = 1 or 2

Answer

Positive = 0

Negative = 1

Answer

Positive = 1 or 2

Negative = 1 or 2

Question 14

How many possible of number of negative zeroes have f (x) = 4x³− 12x² − 5x + 1?

Accepted Answer

1

Answer

0

Answer

3

Answer

2

Question 15

Find the possible number of positive zeroes have f (x) = 2x⁴ + 3x² − 54. Write your answer.

Accepted Answer

1

Question 16

If 𝑧 = 𝑎 + 𝑏𝑖 is a complex zero of a polynomial function of degree more than 1 then the _________ 𝑧̅= 𝑎 − 𝑏𝑖 is also a zero of 𝑓(𝑥) with 𝑏 ≠ 0.

Accepted Answer

CONJUGATE

Question 17

Find all the rational zeroes of 𝑓(𝑥) = 6𝑥⁴ + 11𝑥³ + 5𝑥 + 2 .

Accepted Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$ $,$ $\pm\frac{4}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Question 18

The following are the possible roots of 𝑥³ + 6𝑥² − 160 = 0, except;

Accepted Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Answer

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Question 19

In 𝑓(𝑥) = 𝑥⁴ − 𝑥³ + 5𝑥² − 2𝑥 + 6 has no rational roots.

Accepted Answer

true

Answer

false

Question 20

In 𝑓(𝑥) = 6𝑥⁴ + 11𝑥³ + 5𝑥 + 2, the zeroes function are 2 and $-\frac{1}{3}$ .

Accepted Answer

false

Answer

true

Question 21

Find the end behavior:

$f\left(x\right)\ =\ x^4-2x^2-2x-1$

Accepted Answer

C

Answer

B

Answer

A

Answer

D

Question 22

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

C

Answer

B

Answer

A

Answer

D

Question 23

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

D

Answer

B

Answer

C

Answer

A

Question 24

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

B

Answer

C

Answer

A

Answer

D

Question 25

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

D

Answer

B

Answer

A

Answer

C

Question 26

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

C

Answer

D

Answer

A

Answer

B

Question 27

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 28

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

B

Answer

C

Answer

A

Answer

D

Question 29

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

C

Answer

D

Answer

B

Answer

A

Question 30

$\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{2}{3}$

Accepted Answer

B

Answer

A

Answer

C

Answer

D

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