Answer/Discussion on Solving by Factoring

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Intermediate Algebra
Answer/Discussion to Practice Problems
on Solving 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.

*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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