All Algebra 1 Resources
Example Questions
Example Question #411 : Polynomials
Two consecutive odd numbers have a product of 195. What is the sum of the two numbers?
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 #74 : Polynomials
Factor:
The common factor here is . Pull this out of both terms to simplify:
Example Question #41 : Factoring Polynomials
Factor the following polynomial: .
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: .
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 :
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: .
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:
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:
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: