Algebra 1 : How to factor a variable

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #11 : How To Factor A Variable

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

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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:

Explanation:

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 #11 : How To Factor A Variable

Factor the following polynomial: .

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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 

Example Question #4652 : Algebra 1

Factor the following polynomial: .

Possible Answers:

Correct answer:

Explanation:

Because the  term has a coefficient, you begin by multiplying the  and the  terms () together: 

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

There are four 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 #4653 : Algebra 1

Factor:  

Possible Answers:

Correct answer:

Explanation:

For each term in this expression, we will notice that each shares a variable of .  This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:  

Example Question #4654 : Algebra 1

Factor:  

Possible Answers:

Correct answer:

Explanation:

For each term in this expression, we will notice that each shares a variable of .  This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:  

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