Scroll:Algebra new >> Rational expression >> ps (4123)


Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

 Which rational expression should be subtracted from to get 

 3x3 - 7x2 + 4

----------------

4x - 3


to get 2x2 - 5x + 2       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




2)  

 Which rational expression should be subtracted from to get 

 4x3 - 7x2 + 3

----------------

3x - 3


to get 3x2 - 5x + 2       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




3)  

 Which rational expression should be subtracted from to get 

 3x3 - 6x2 + 3

----------------

2x - 3


to get 2x2 - 5x + 2       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




4)  

 Which rational expression should be subtracted from to get 

 3x3 - 5x2 + 6

----------------

3x - 3


to get 3x2 - 4x + 2       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




5)  

 Which rational expression should be subtracted from to get 

 4x3 - 6x2 + 6

----------------

2x - 1


to get 2x2 - 4x + 2       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




6)  

 Which rational expression should be subtracted from to get 

 3x3 - 5x2 + 4

----------------

4x - 3


to get 3x2 - 4x + 1       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




7)  

 Which rational expression should be subtracted from to get 

 4x3 - 4x2 + 4

----------------

2x - 3


to get 3x2 - 5x + 2       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




8)  

 Which rational expression should be subtracted from to get 

 2x3 - 6x2 + 3

----------------

4x - 3


to get 2x2 - 3x + 1       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




9)  

 Which rational expression should be subtracted from to get 

 4x3 - 5x2 + 3

----------------

4x - 2


to get 2x2 - 3x + 1       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




10)  

 Which rational expression should be subtracted from to get 

 2x3 - 4x2 + 3

----------------

2x - 3


to get 2x2 - 3x + 1       Write the answer like  + or -

   X3  =   x3 

  X 2  =   x2

   X      =   x  

 unite  =  

 

X  =   x

unite =  

 


Answer:_______________




 

1)  

 Which rational expression should be subtracted from to get 

 3x3 - 7x2 + 4

----------------

4x - 3


to get 2x2 - 5x + 2       Write the answer like  + or -

   X3  =   Answer: -5x3 

  X 2  =   Answer: +11x2

   X      =   Answer: -14x  

 unite  =   Answer: +10

 

X  =   Answer: 4 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 3x3 - 7x2 + 4

----------------

4x - 3

- p(x) =2x2 - 5x + 2

 

 3x3 - 7x2 + 4 - (2x2 - 5x + 2) (4x-3)

------------------------------------

4x - 3

 

(3x3 - 7x2 + 4) - (8x3 - 10x2 + 4x - 8x+ 10x - 6)

--------------------------------------------------------

4x  - 3

 

⇒ 

3x3 - 7x2 + 4 - 8x3 - 14x + 18x2 + 6

------------------------------------------------

4x  - 3

Answer is

-5x3 + 11x2 - 14x + 10

----------------------

4x  - 3

 



2)  

 Which rational expression should be subtracted from to get 

 4x3 - 7x2 + 3

----------------

3x - 3


to get 3x2 - 5x + 2       Write the answer like  + or -

   X3  =   Answer: -5x3 

  X 2  =   Answer: +14x2

   X      =   Answer: -16x  

 unite  =   Answer: +9

 

X  =   Answer: 3 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 4x3 - 7x2 + 3

----------------

3x - 3

- p(x) =3x2 - 5x + 2

 

 4x3 - 7x2 + 3 - (3x2 - 5x + 2) (3x-3)

------------------------------------

3x - 3

 

(4x3 - 7x2 + 3) - (9x3 - 15x2 + 6x - 6x+ 10x - 6)

--------------------------------------------------------

3x  - 3

 

⇒ 

4x3 - 7x2 + 3 - 9x3 - 16x + 21x2 + 6

------------------------------------------------

3x  - 3

Answer is

-5x3 + 14x2 - 16x + 9

----------------------

3x  - 3

 



3)  

 Which rational expression should be subtracted from to get 

 3x3 - 6x2 + 3

----------------

2x - 3


to get 2x2 - 5x + 2       Write the answer like  + or -

   X3  =   Answer: -1x3 

  X 2  =   Answer: +8x2

   X      =   Answer: -14x  

 unite  =   Answer: +9

 

X  =   Answer: 2 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 3x3 - 6x2 + 3

----------------

2x - 3

- p(x) =2x2 - 5x + 2

 

 3x3 - 6x2 + 3 - (2x2 - 5x + 2) (2x-3)

------------------------------------

2x - 3

 

(3x3 - 6x2 + 3) - (4x3 - 10x2 + 4x - 4x+ 10x - 6)

--------------------------------------------------------

2x  - 3

 

⇒ 

3x3 - 6x2 + 3 - 4x3 - 14x + 14x2 + 6

------------------------------------------------

2x  - 3

Answer is

-1x3 + 8x2 - 14x + 9

----------------------

2x  - 3

 



4)  

 Which rational expression should be subtracted from to get 

 3x3 - 5x2 + 6

----------------

3x - 3


to get 3x2 - 4x + 2       Write the answer like  + or -

   X3  =   Answer: -6x3 

  X 2  =   Answer: +13x2

   X      =   Answer: -14x  

 unite  =   Answer: +12

 

X  =   Answer: 3 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 3x3 - 5x2 + 6

----------------

3x - 3

- p(x) =3x2 - 4x + 2

 

 3x3 - 5x2 + 6 - (3x2 - 4x + 2) (3x-3)

------------------------------------

3x - 3

 

(3x3 - 5x2 + 6) - (9x3 - 12x2 + 6x - 6x+ 8x - 6)

--------------------------------------------------------

3x  - 3

 

⇒ 

3x3 - 5x2 + 6 - 9x3 - 14x + 18x2 + 6

------------------------------------------------

3x  - 3

Answer is

-6x3 + 13x2 - 14x + 12

----------------------

3x  - 3

 



5)  

 Which rational expression should be subtracted from to get 

 4x3 - 6x2 + 6

----------------

2x - 1


to get 2x2 - 4x + 2       Write the answer like  + or -

   X3  =   Answer: -0x3 

  X 2  =   Answer: +6x2

   X      =   Answer: -12x  

 unite  =   Answer: +8

 

X  =   Answer: 2 x

unite = Answer: -1 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 4x3 - 6x2 + 6

----------------

2x - 1

- p(x) =2x2 - 4x + 2

 

 4x3 - 6x2 + 6 - (2x2 - 4x + 2) (2x-1)

------------------------------------

2x - 1

 

(4x3 - 6x2 + 6) - (4x3 - 8x2 + 4x - 4x+ 8x - 2)

--------------------------------------------------------

2x  - 1

 

⇒ 

4x3 - 6x2 + 6 - 4x3 - 12x + 12x2 + 2

------------------------------------------------

2x  - 1

Answer is

-0x3 + 6x2 - 12x + 8

----------------------

2x  - 1

 



6)  

 Which rational expression should be subtracted from to get 

 3x3 - 5x2 + 4

----------------

4x - 3


to get 3x2 - 4x + 1       Write the answer like  + or -

   X3  =   Answer: -9x3 

  X 2  =   Answer: +11x2

   X      =   Answer: -7x  

 unite  =   Answer: +7

 

X  =   Answer: 4 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 3x3 - 5x2 + 4

----------------

4x - 3

- p(x) =3x2 - 4x + 1

 

 3x3 - 5x2 + 4 - (3x2 - 4x + 1) (4x-3)

------------------------------------

4x - 3

 

(3x3 - 5x2 + 4) - (12x3 - 12x2 + 3x - 4x+ 4x - 3)

--------------------------------------------------------

4x  - 3

 

⇒ 

3x3 - 5x2 + 4 - 12x3 - 7x + 16x2 + 3

------------------------------------------------

4x  - 3

Answer is

-9x3 + 11x2 - 7x + 7

----------------------

4x  - 3

 



7)  

 Which rational expression should be subtracted from to get 

 4x3 - 4x2 + 4

----------------

2x - 3


to get 3x2 - 5x + 2       Write the answer like  + or -

   X3  =   Answer: -2x3 

  X 2  =   Answer: +15x2

   X      =   Answer: -16x  

 unite  =   Answer: +10

 

X  =   Answer: 2 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 4x3 - 4x2 + 4

----------------

2x - 3

- p(x) =3x2 - 5x + 2

 

 4x3 - 4x2 + 4 - (3x2 - 5x + 2) (2x-3)

------------------------------------

2x - 3

 

(4x3 - 4x2 + 4) - (6x3 - 15x2 + 6x - 4x+ 10x - 6)

--------------------------------------------------------

2x  - 3

 

⇒ 

4x3 - 4x2 + 4 - 6x3 - 16x + 19x2 + 6

------------------------------------------------

2x  - 3

Answer is

-2x3 + 15x2 - 16x + 10

----------------------

2x  - 3

 



8)  

 Which rational expression should be subtracted from to get 

 2x3 - 6x2 + 3

----------------

4x - 3


to get 2x2 - 3x + 1       Write the answer like  + or -

   X3  =   Answer: -6x3 

  X 2  =   Answer: +4x2

   X      =   Answer: -5x  

 unite  =   Answer: +6

 

X  =   Answer: 4 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 2x3 - 6x2 + 3

----------------

4x - 3

- p(x) =2x2 - 3x + 1

 

 2x3 - 6x2 + 3 - (2x2 - 3x + 1) (4x-3)

------------------------------------

4x - 3

 

(2x3 - 6x2 + 3) - (8x3 - 6x2 + 2x - 4x+ 3x - 3)

--------------------------------------------------------

4x  - 3

 

⇒ 

2x3 - 6x2 + 3 - 8x3 - 5x + 10x2 + 3

------------------------------------------------

4x  - 3

Answer is

-6x3 + 4x2 - 5x + 6

----------------------

4x  - 3

 



9)  

 Which rational expression should be subtracted from to get 

 4x3 - 5x2 + 3

----------------

4x - 2


to get 2x2 - 3x + 1       Write the answer like  + or -

   X3  =   Answer: -4x3 

  X 2  =   Answer: +5x2

   X      =   Answer: -5x  

 unite  =   Answer: +5

 

X  =   Answer: 4 x

unite = Answer: -2 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 4x3 - 5x2 + 3

----------------

4x - 2

- p(x) =2x2 - 3x + 1

 

 4x3 - 5x2 + 3 - (2x2 - 3x + 1) (4x-2)

------------------------------------

4x - 2

 

(4x3 - 5x2 + 3) - (8x3 - 6x2 + 2x - 4x+ 3x - 2)

--------------------------------------------------------

4x  - 2

 

⇒ 

4x3 - 5x2 + 3 - 8x3 - 5x + 10x2 + 2

------------------------------------------------

4x  - 2

Answer is

-4x3 + 5x2 - 5x + 5

----------------------

4x  - 2

 



10)  

 Which rational expression should be subtracted from to get 

 2x3 - 4x2 + 3

----------------

2x - 3


to get 2x2 - 3x + 1       Write the answer like  + or -

   X3  =   Answer: -2x3 

  X 2  =   Answer: +4x2

   X      =   Answer: -5x  

 unite  =   Answer: +6

 

X  =   Answer: 2 x

unite = Answer: -3 

 


SOLUTION 1 :

 

Solution :

Let p(x) be the required rational expression.

Given that 

 

 2x3 - 4x2 + 3

----------------

2x - 3

- p(x) =2x2 - 3x + 1

 

 2x3 - 4x2 + 3 - (2x2 - 3x + 1) (2x-3)

------------------------------------

2x - 3

 

(2x3 - 4x2 + 3) - (4x3 - 6x2 + 2x - 2x+ 3x - 3)

--------------------------------------------------------

2x  - 3

 

⇒ 

2x3 - 4x2 + 3 - 4x3 - 5x + 8x2 + 3

------------------------------------------------

2x  - 3

Answer is

-2x3 + 4x2 - 5x + 6

----------------------

2x  - 3