Question 1

Find all the zeroes of the function $f\left(x\right)\ =\ x^3-4x^2-5x$ using rational zero theorem.

Accepted Answer

5, -1, 0

Answer

5, 1, 0

Answer

-5, -1, 0

Answer

-5, 1, 0

Question 2

Find all the possible roots of the function $f\left(x\right)\ =\ x^3-4x^2-5x$

Accepted Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Question 3

The following are the possible roots of the function $f\left(x\right)\ =\ x^3-4x^2-5x$ , except:

Accepted Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Question 4

Find all the zeroes in the function $f\left(x\right)\ =\ x^3-4x^2-5x$ .

Accepted Answer

2, $f\left(x\right)\ =\ x^3-4x^2-5x$ , -5

Answer

$\pm1,\ \pm2,\ \pm3,\ \pm6$

Answer

-2, 2, -5

Answer

3, $f\left(x\right)\ =\ x^3-4x^2-5x$ , -2

Question 5

The following are the zeroes of the function $f\left(x\right)\ =\ x^3-4x^2-5x$ except;

Accepted Answer

2

Answer

-4

Answer

3

Answer

1

Question 6

Which of the following statements is considered incorrect?

Accepted Answer

All possible rational roots will leads us to find zeroes, remainder and factors of polynomials.

Answer

Factor theorem is an easy way basis of factoring polynomials, given the other factor.

Answer

The highest exponent on a function will same as how many zeroes are in the function.

Answer

Synthetic division is an easy way to test all the theorems correctly.

Question 7

Using remainder theorem, find the remainder in the function : $f\left(x\right)\ =\ x^3-4x^2-5x$

Accepted Answer

-3

Answer

-2

Answer

3

Answer

2

Question 8

Find the remainder in the function, $f\left(x\right)\ =\ x^3-4x^2-5x$

Accepted Answer

-4

Answer

14

Answer

-14

Answer

4

Question 9

Given at x = 7. Find the remainder in the function: $f\left(x\right)\ =\ x^3-4x^2-5x$

Accepted Answer

10

Answer

15

Answer

-20

Answer

-10

Question 10

Divide the function using the synthetic method and find the remainder:

$f\left(x\right)\ =\left(\ x^4+11x^3+33x^2+24x+32\right)\ \div\ \left(x+6\right)$

Accepted Answer

-4

Answer

4

Answer

2

Answer

-6

Question 11

Divide

$f\left(v\right)\ =\ \left(8v^5+32v^4+5v+20\right)\div\left(v+4\right)$

and find the remainder.

Accepted Answer

0

Answer

12

Answer

-4

Answer

-6

Question 12

Which of the following are the factors of the function, $f\left(x\right)\ =\ x^3-4x^2-5x$ .

Accepted Answer

(y + 5)(y + 4)

Answer

(y - 10)(y - 2)

Answer

(y + 10)(y + 2)

Answer

(y - 5)(y - 4)

Question 13

Find the other factor of $f\left(x\right)\ =\ x^3-4x^2-5x$ , if other factor is x -3.

Accepted Answer

x - 8

Answer

x + 8

Answer

x + 6

Answer

x - 6

Question 14

Statement: $f\left(x\right)\ =\ x^3-4x^2-5x$ is a polynomials with one factor which is x + 6.

Accepted Answer

False, it is not factorable.

Answer

True, we find it by using factor theorem with synthetic division. We substitute x = -6

Answer

True, and the other factor is x +6, also.

Answer

False, it is negative. The correct factor is x - 6.

Question 15

(x + 1) is a factor of $f\left(x\right)\ =\ x^3-4x^2-5x$

Accepted Answer

YES

Answer

NEITHER

Answer

UNDEFINED

Answer

NO

Question 16

State the function $f\left(x\right)\ =\ x^3-4x^2-5x$ is a factor of (k -2).

Accepted Answer

YES, It is one of a factor.

Answer

NO, the polynomials are not factorable.

Answer

YES, and the other factor are (k+1) and (k-1).

Answer

NO, It is not a factor.

Question 17

Given A = L x W of a rectangle, find the area of it if the length is x -4 and the width is x + 8.

Accepted Answer

A = $f\left(x\right)\ =\ x^3-4x^2-5x$

Answer

A = $f\left(x\right)\ =\ x^3-4x^2-5x$

Answer

A = $f\left(x\right)\ =\ x^3-4x^2-5x$

Answer

A = $f\left(x\right)\ =\ x^3-4x^2-5x$

Question 18

The area of the rectangle is $f\left(x\right)\ =\ x^3-4x^2-5x$ . The width is x - 8. Find the lenght.

Accepted Answer

L = x - 9

Answer

L = x + 11

Answer

L = x - 11

Answer

L = x + 9

Question 19

Find the two consecutive odd whole numbers whose product is 63.

Accepted Answer

7 and 9

Answer

5 and 9

Answer

13 and 15

Answer

11 and 13

Question 20

The children equally divided into x -1 to enter in the park. All of the children composed of 4x³- 9x²+ 9x + 3. How many chidren were not included to enter, since they are only not equally divided?

Accepted Answer

7 children

Answer

8 children

Answer

6 children

Answer

5 children

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