1. SOLVING RADICAL EQUATIONS WITH EXTRANEOUS SOLUTIONS Unit 2E Day 5

2. Do now  Determine whether or not the radical is isolated. 

3. Review Factoring  Factoring means rewriting as a ____________  x 2 + bx + c (leading coefficient 1)  We need to find two numbers (m and n) that multiply to _____ and add to _____.  Then the factored form is (x + m)(x + n).  Factor x 2 + 2x – 3.

4. Review the Zero Product  If two factors multiply to get zero, then at least one of the factors must be equal to ________.  Find the value of x:  (x + 2)(x + 3) = 0

5. Review Square Roots  Remember that when YOU take the square root, you answer needs to include ______________.  Ex: x 2 = 9 x = ____  However, if the square root is ALREADY THERE, it is DEFINED to be __________.  Ex: x = √9 x = ____

6. Solving Radical Equations with x Outside the Radical  Ex. 1: Solve the radical equation 1.Isolate the radical (already done) 2.Square both sides to eliminate the radical. 3.Get all the variables to one side. 4.Factor! 5.Use ZPP to solve for x (set each set of parentheses equal to zero) 6.CHECK YOUR ANSWERS.

7. Extraneous Solutions  An extraneous solution is a solution that comes from the process of solving the problem but is not a valid solution to the original problem  Does not mean you made a mistake  This is why it is very important to ________________!

8. Solving Radical Equations with x Outside the Radical  Ex. 2: Solve the radical equation 1.Isolate the radical (already done) 2.Square both sides to eliminate the radical. 3.Get all the variables to one side. 4.Factor! 5.Use ZPP to solve for x (set each set of parentheses equal to zero) 6.CHECK YOUR ANSWERS.

9. Solving Radical Equations with x Outside the Radical  Ex. 3: Solve the radical equation 1.Isolate the radical (already done) 2.Square both sides to eliminate the radical. 3.Get all the variables to one side. 4.Factor! 5.Use ZPP to solve for x (set each set of parentheses equal to zero) 6.CHECK YOUR ANSWERS.

10. Solving Radical Equations with x Outside the Radical  Ex. 4: Solve the radical equation 1.Isolate the radical (already done) 2.Square both sides to eliminate the radical. 3.Get all the variables to one side. 4.Factor! 5.Use ZPP to solve for x (set each set of parentheses equal to zero) 6.CHECK YOUR ANSWERS.

11. Solving Radical Equations with x Outside the Radical  Ex. 5: Solve the radical equation 1.Isolate the radical (already done) 2.Square both sides to eliminate the radical. 3.Get all the variables to one side. 4.Factor! 5.Use ZPP to solve for x (set each set of parentheses equal to zero) 6.CHECK YOUR ANSWERS.