GRE Subject Test: Math : Classifying Algebraic Functions
Study concepts, example questions & explanations for GRE Subject Test: Math
All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Roots Of Polynomials
What are the roots of the polynomial: 
None of the Above
Step 1: Find factors of 44:
Step 2: Find which pair of factors can give me the middle number. We will choose 
Step 3: Using 
Step 4: Write the factored form of that trinomial:
Step 5: To solve for x, you set each parentheses to 
The solutions to this equation are 
Example Question #2 : Roots Of Polynomials
Solve for 
Step 1: Factor by pairs:
Step 2: Re-write the factorization:
Step 3: Solve for x:
Example Question #1 : Roots Of Polynomials
Find 
No Solutions Exist
Step 1: Find two numbers that multiply to 
We will choose 
Step 2: Factor using the numbers we chose:
Step 3: Solve each parentheses for each value of x..
Example Question #3 : Roots Of Polynomials
Based upon the fundamental theorem of algebra, we know that there must exist 3 roots for this polynomial based upon its' degree of 3.
To solve for the roots, we use factor by grouping:
First group the terms into two binomials:
Then take out the greatest common factor from each group:
Now we see that the leftover binomial is the greatest common factor itself:
We set each binomial equal to zero and solve:
Example Question #1 : Classifying Algebraic Functions
Find all of the roots for the polynomial below:
In order to find the roots for the polynomial we must first put it in Standard Form by decreasing exponent:
Now we can use factor by grouping, we start by grouping the 4 terms into 2 binomials:
We now take the greatest common factor out of each binomial:
We can see that each term now has the same binomial as a common factor, so we simplify to get:
To find all of the roots, we set each factor equal to zero and solve:
Example Question #5 : Roots Of Polynomials
Example Question #1 : Algebra
What are the roots of 
Step 1: Find two numbers that multiply to 
We will choose
Check:
We have the correct numbers...
Step 2: Factor the polynomial...
Step 3: Set the parentheses equal to zero to get the roots...
So, the roots are 
Example Question #4 : Algebra
Find all of the roots for the polynomial below:
In order to find the roots of the polynomial we must factor by grouping:
Group into two binomials:
Take out the greatest common factor from each binomial:
We can now see that each term has a common binomial factor:
We set each factor equal to zero and solve to obtain the roots:
Example Question #1 : Binomial Expansion
Expand: 
Step 1: Evaluate 
Step 2. Evaluate
From the previous step, we already know what 
Step 3: Evaluate 
The expansion of 
Example Question #2 : Binomial Expansion
What is the expansion of 
Solution:
We can look at Pascal's Triangle, which is a quick way to do Binomial Expansion. We read each row (across, left to right)
For the first row, we only have a constant.
For the second row, we get 
...
For the 7th row, we will start with an 
Step 1: We need to locate the 7th row of the triangle and write the numbers in that row out.
The 7th row is 
Step 2: If we translate the 7th row into an equation, we get:
All GRE Subject Test: Math Resources
