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Answer/Discussion to 1a

 

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.

 

*Factor the difference of squares

 

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.

 

(return to problem 1a)

 

 

Answer/Discussion to 1b

 

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.

 

*Factor a GCF out

 

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.

 

(return to problem 1b)

 

 

Answer/Discussion to 1c

 

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.

 

*Factor the trinomial

 

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.

 

(return to problem 1c)

 

 

Answer/Discussion to 1d

 

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.

 

*Factor the trinomial

 

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.

 

(return to problem 1d)

 

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Last revised on July 1, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.