Intermediate Algebra Tutorial 30


Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 30: Solve by Factoring


WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 30: Solve by Factoring


 

checkAnswer/Discussion to 1a

problem 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.

 
ad1a1

*Factor the difference of squares

 
Step 4: Use the Zero Factor Property

AND

Step 5: Solve for the equations set up in step 4.

 
ad1a2
*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)

 


 

checkAnswer/Discussion to 1b

problem 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.

 
ad1b1

*Factor a GCF out

 
Step 4: Use the Zero Factor Property

AND

Step 5: Solve for the equations set up in step 4.

 
ad1c1

 

*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)

 


 

checkAnswer/Discussion to 1c

problem 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.

 
ad1c1
*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.

 
ad1c2
*Get polynomial = 0 

 
Step 3: Factor the Polynomial.

 
ad1c3
*Factor the trinomial

 
Step 4: Use the Zero Factor Property

AND

Step 5: Solve for the equations set up in step 4.

 
ad1c4

*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)

 


 

checkAnswer/Discussion to 1d

problem 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.

 
ad1d1
*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.

 
ad1d2
*Get polynomial = 0 

 
Step 3: Factor the Polynomial.

 
ad1d3
*Factor the trinomial

 
Step 4: Use the Zero Factor Property

AND

Step 5: Solve for the equations set up in step 4.

 
ad1d4
*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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WTAMU > Virtual Math Lab >Intermediate Algebra >Tutorial 30: Solve by Factoring


Last revised on July 1, 2011 by Kim Seward.
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