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 expression by grouping.

6.    Factorise the quadratic expression by completing the square.

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

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

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 expression by 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,    