Algebra Knowledge Examples

 

Lets assume that the student asked what the solution to the below questions.

 

Questions:

1.    For what values of  is the expression  not defined?

2.    Simplify the expression .

3.    Rewrite the inequality in terms of x.

4.    Expand and simplify the expression .

5.    Factorise the expressionby grouping.

6.    Factorise the quadratic expression by completing the square.

7.    Find the roots of the quadratic expression  by using the quadratic formula. 

 

Answer:

 

You can solve these questions by seeing the solutions to the given questions which also uses the quotient rule.

 

 

Questions which will help you to solve your questions

 

Question 1: For what values of  is the expression  not defined?

 

Answer: The expression is not defined when the denominator equals to zero. That is:

              

              

              

              

 

·        What is the denominator in your question?

 

·        When does the denominator equal to zero?

 


 

Question 2: Simplify the expression .

 

Answer:

                                       

                                       

                                       

 

 

Question 3: Rewrite the inequality  in terms of x.

Answer:    

                  

                  

                    

                    

                            

                    

Note that division by a negative number or multiplication by a negative number changes the direction of the inequality sign.

 

Question 4: Expand and simplify the expression .

 

Answer:

                                                  

                                                  

       

Question 5: Factorise the expressionby grouping.

 

Answer:

                                           

                                           

 

 

Question 6: Factorise the quadratic expression by completing the square.

 

Answer:

              

              

              

              

             

             

              

              

              

                     and    

                           and    

 

Question 7: Find the roots of the quadratic expression  by using the quadratic formula. 

 

Answer: If   then    

                  

Hence,