3 6 Title

Intermediate Algebra
Tutorial 30: Solve by Factoring

 Step 1: Simplify if needed.

 In this problem, there is no simplifying that we can do.

 Step 2: Write in standard form if needed.

 This problem is already written in standard form.

 Step 3: Factor the Polynomial.

 Step 4: Use the Zero Factor Property AND
 Step 5: Solve for the equations set up in step 4.

 *Set 1st factor = 0 *Solve for a             *Set 2nd factor = 0 *Solve for a

 The solutions to this equation are -3/4 and 3/4. Note that if we plug either of these numbers into the original equation, they would make the left side equal to the right side.

 Step 1: Simplify if needed.

 In this problem, there is no simplifying that we can do.

 Step 2: Write in standard form if needed.

 This problem is already written in standard form.

 Step 3: Factor the Polynomial.

 Step 4: Use the Zero Factor Property AND
 Step 5: Solve for the equations set up in step 4.

 *Set 1st factor = 0 *Solve for x       *Set 2nd factor = 0 *Solve for x

 The solutions to this equation are 0 and 4/3. Note that if we plug either of these numbers into the original equation, they would make the left side equal to the right side.

 Step 1: Simplify if needed.

 We can simplify this problem by multiplying both sides of the equation by the LCD.  This will clear out the fractions and make it a nicer problem to work with.

 *Multiply both sides by LCD 4

 Step 2: Write in standard form if needed.

 This problem is not written in standard form.  We need to move the -2r and 1 over to the other side of this equation so we have the polynomial set equal to 0.

 *Get polynomial = 0

 Step 3: Factor the Polynomial.

 Step 4: Use the Zero Factor Property AND
 Step 5: Solve for the equations set up in step 4.

 *Set 1st factor = 0 *Solve for r             *Set 2nd factor = 0 *Solve for r

 The solutions to this equation are 1/4 and -1/2. Note that if we plug either of these numbers into the original equation, they would make the left side equal the right side.

 Step 1: Simplify if needed.

 On this problem you need to be careful.  Since it is set equal to -6, it is NOT in standard form.  So we need to multiply the left side out and then get it into standard form.

 *Use the FOIL method to multiply

 Step 2: Write in standard form if needed.

 This problem is not written in standard form.  We need to move the -6 over to the other side of this equation so we have the polynomial set equal to 0.

 *Get polynomial = 0

 Step 3: Factor the Polynomial.

 Step 4: Use the Zero Factor Property AND
 Step 5: Solve for the equations set up in step 4.

 *Set 1st factor = 0 *Solve for x     *Set 2nd factor = 0 *Solve for x

 The solutions to this equation are 2 and 1. Note that if we plug either of these numbers into the original equation, they would make the left side equal to the right side.

Last revised on July 1, 2011 by Kim Seward.