Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 30: Solve by Factoring
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. 
Step 5: Solve for the equations set up in step 4. 
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. 
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. 
Step 5: Solve for the equations set up in step 4. 
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. 
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. 
Step 3: Factor the Polynomial. 
Step 5: Solve for the equations set up in step 4. 
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. 
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. 
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. 
Step 3: Factor the Polynomial. 
Step 5: Solve for the equations set up in step 4. 
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.
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