Intermediate Algebra Exercises Section 5.4 Division

 

EXERCISES

1) Use long division to find the quotient and remainder when 5x2 -17x -12 is divided by x - 4.

2) Use long division to find the quotient and remainder when 6x3 - 16x2 + 17x - 6 is divided by 3x - 2.

3) Use long division to find the quotient and remainder when x4 + 5x3 + 6x2 -x - 2 is divided by x+ 2.

4) Use long division to find the quotient and remainder when x3 + 2x2 - 5x - 4 is divided by x+ .

5) Use long division to find the quotient and remainder when x4 + 6x3 + 11x2 + 6x is divided by x2 +3x+ 2.

6) Use long division to find the quotient and remainder when is divided by .

SOLUTIONS

1) Use long division to find the quotient and remainder when 5x2 -17x -12 is divided by x - 4.
Solution:      
What can we conclude from this?
This process has revealed the quotient 5x + 3 and remainder 0 as assured by the Division Algorithm.
Now we know      5x2 - 17x -12 = (x - 4)(5x + 3)

2) Use long division to find the quotient and remainder when 6x3 - 16x2 + 17x - 6 is divided by 3x - 2.
Solution:      
What can we conclude from this?
This process has revealed the quotient 2x2 - 4x + 3 and remainder 0 as assured by the Division Algorithm.
Now we know   6x3 - 16x2 + 17x - 6 = (3x - 2)(2x2 - 4x + 3)

3) Use long division to find the quotient and remainder when x4 + 5x3 + 6x2 -x - 2 is divided by x+ 2.
Solution:      
What can we conclude from this?
This process has revealed the quotient x3 + 3x2- 1 and remainder 0 as assured by the Division Algorithm.
Now we know   x4 + 5x3 + 6x2 -x - 2 = (x+2)(x3 + 3x2- 1)

4) Use long division to find the quotient and remainder when x3 + 2x2 - 5x - 4 is divided by x+ .
Solution:      
What can we conclude from this?
This process has revealed the quotient and remainder 6 as assured by the Division Algorithm.
Now we know  

  

5) Use long division to find the quotient and remainder when x4 + 6x3 + 11x2 + 6x is divided by x2 +3x+ 2.
Solution:      
What can we conclude from this?
This process has revealed the quotient x2 + 3x and remainder 0 as assured by the Division Algorithm.
Now we know   x4 + 6x3 + 11x2+ 6x = (x2 + 3x)(x2 + 3x + 2)
We can factor each of these quadratic polynomials so that we get
x4 + 6x3 + 11x2+ 6x = (x2 + 3x)(x2 + 3x + 2) = x(x + 3)(x+ 1)(x + 2)

6) Use long division to find the quotient and remainder when is divided by .
Solution:      
What can we conclude from this?
This process has revealed the quotient and remainder as assured by the Division Algorithm.
Now we know