College Algebra 1.4 I. Radical Equations; II. Equations Quadratic in Form; III. Factorable Equations

I. Solving Radical Equations 1. Isolate a radical. 2. Raise each SIDE to the appropriate power ( square a square root, cube a cube root, etc .) and simplify. 3. (Repeat until no radicals remain.) 4. Solve the resulting equation. 5. CHECK for EXTRANEOUS SOLUTIONS. Note: Extraneous solutions are solutions which do not solve the original equation. They are Extra(neous).

1. Isolate a radical.

2. Raise each SIDE to the appropriate power

( square a square root, cube a cube root, etc .) and simplify.

3. (Repeat until no radicals remain.)

4. Solve the resulting equation.

5. CHECK for EXTRANEOUS SOLUTIONS.

Note: Extraneous solutions are solutions which do not solve the original equation. They are Extra(neous).

extraneous solution (does not work in the original equation)

II. “Quadratic Form” Equations – The degree of one term is twice the degree of the other term. Method 1: Substitution 1. Substitute another variable, say u, for the original variable to obtain the form: au 2 + bu + c = 0 2. Solve this quadratic equation (for u) using any method you wish. 3. Substitute the solutions for u to find the solutions for the original variable.

Method 1: Substitution

1. Substitute another variable, say u, for the original variable to obtain the form:

au 2 + bu + c = 0

2. Solve this quadratic equation (for u) using

any method you wish.

3. Substitute the solutions for u to find the

solutions for the original variable.

III. Higher Degree Polynomial Equations ● Try to solve by Factoring. ● Remember to first look for a ___________ ● Remember the different methods of Factoring for different situations: trinomials, difference of squares, sum/difference of cubes, grouping, etc. ● Remember that the solutions to f(x)= 0 are: ________________________________

● Try to solve by Factoring.

● Remember to first look for a ___________

● Remember the different methods of Factoring for different situations: trinomials, difference of squares, sum/difference of cubes, grouping, etc.

● Remember that the solutions to f(x)= 0 are: ________________________________

Solve the equation: