### All Algebra 1 Resources

## Example Questions

### Example Question #3 : How To Factor A Variable

Solve for .

**Possible Answers:**

**Correct answer:**

Multiply both sides by 3:

Distribute:

Subtract from both sides:

Add the terms together, and subtract from both sides:

Divide both sides by :

Simplify:

### Example Question #5 : How To Factor A Variable

Factor the following polynomical expression completely, using the "factor-by-grouping" method.

**Possible Answers:**

**Correct answer:**

Let's split the four terms into two groups, and find the GCF of each group.

First group:

Second group:

The GCF of the first group is . When we divide the first group's terms by , we get: .

The GCF of the second group is . When we divide the second group's terms by , we get: .

We can rewrite the original expression,

as,

The common factor for BOTH of these terms is .

Dividing both sides by gives us:

### Example Question #4 : How To Factor A Variable

Factor the following polynomial expression completely, using the "factor-by-grouping" method.

**Possible Answers:**

**Correct answer:**

Let's separate the four terms of the polynomial expression into two groups, and then find the GCF (greatest common factor) for each group.

First group:

Second group:

The GCF of the first group is ; it's the only factor both terms have in common. Factoring the first group by its GCF gives us:

The second group is a bit tricky. It looks like they have no factor in common. But, each of the terms can be divided by ! So, the GCF is .

Factoring the second group by its GCF gives us:

We can rewrite the original expression:

is the same as:

,

which is the same as:

### Example Question #5 : How To Factor A Variable

Factor the following polynomial expression completely, using the "factor-by-grouping" method.

**Possible Answers:**

**Correct answer:**

Separate the four terms into two groups, and then find the GCF of each group.

First group:

Second group:

The GCF of the first group is . Factoring out from the terms in the first group gives us:

The GCF of the second group is . Factoring out from the terms in the second group gives us:

We can rewrite the original expression,

as,

We can factor this as:

### Example Question #7 : How To Factor A Variable

Factor the polynomial expression completely, using the "factor-by-grouping" method.

**Possible Answers:**

**Correct answer:**

Start by separating the four terms into two groups, and find the GCF (greatest common factor) of each group.

First group:

Second group:

The GCF of the first group is . By factoring out from each term in the first group, we are left with:

(Remember, when dividing by a negative, the original number changes its sign!)

The GCF of the second group is . By factoring out from each term in the second group, we get:

We can rewrite the original expression,

as,

The GCF of each of these terms is...

,

...so, the expression, when factored, is:

### Example Question #1213 : Algebra Ii

Two consecutive odd numbers have a product of 195. What is the sum of the two numbers?

**Possible Answers:**

**Correct answer:**

You can set the two numbers to equal variables, so that you can set up the algebra in this problem. The first odd number can be defined as and the second odd number, since the two numbers are consecutive, will be .

This allows you to set up the following equation to include the given product of 195:

Next you can subtract 195 to the left and set the equation equal to 0, which allows you to solve for :

You can factor this quadratic equation by determining which factors of 195 add up to 2. Keep in mind they will need to have opposite signs to result in a product of negative 195:

Set each binomial equal to 0 and solve for . For the purpose of this problem, you'll only make use of the positive value for :

Now that you have solved for , you know the two consecutive odd numbers are 13 and 15. You solve for the answer by finding the sum of these two numbers:

### Example Question #12 : How To Factor A Variable

Factor:

**Possible Answers:**

**Correct answer:**

The common factor here is . Pull this out of both terms to simplify:

### Example Question #41 : Factoring Polynomials

Factor the following polynomial: .

**Possible Answers:**

**Correct answer:**

Because the term doesn’t have a coefficient, you want to begin by looking at the term () of the polynomial: . Find the factors of that when added together equal the second coefficient (the term) of the polynomial.

There are only four factors of : , and only two of those factors, , can be manipulated to equal when added together and manipulated to equal when multiplied together: (i.e.,).

### Example Question #42 : Factoring Polynomials

Factor the following polynomial: .

**Possible Answers:**

**Correct answer:**

Because the term doesn’t have a coefficient, you want to begin by looking at the term () of the polynomial: .

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

There are seven factors of : , and only two of those factors, , can be manipulated to equal when added together and manipulated to equal when multiplied together:

### Example Question #13 : How To Factor A Variable

Solve for when :

**Possible Answers:**

**Correct answer:**

First, factor the numerator: .

Now your expression looks like

Second, cancel the "like" terms - - which leaves us with .

Third, solve for , which leaves you with .

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