GRE Subject Test: Math : Roots of Polynomials

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Algebra

What are the roots of the polynomial: ?

Possible Answers:

None of the Above

Correct answer:

Explanation:

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  and , we need to get . The only way to get  is if I have  and .

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  and .

Example Question #1 : Classifying Algebraic Functions

Solve for

Possible Answers:

Correct answer:

Explanation:

Step 1: Factor by pairs:





Step 2: Re-write the factorization:  



Step 3: Solve for x:


Example Question #2 : Classifying Algebraic Functions

Find

Possible Answers:

No Solutions Exist

Correct answer:

Explanation:

Step 1: Find two numbers that multiply to  and add 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 : Classifying Algebraic Functions

Possible Answers:

Correct answer:

Explanation:

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 #4 : Classifying Algebraic Functions

Find all of the roots for the polynomial below: 

Possible Answers:

Correct answer:

Explanation:

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 #5 : Classifying Algebraic Functions

Find all of the roots for the polynomial below: 

Possible Answers:

Correct answer:

Explanation:

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 #1 : Roots Of Polynomials

Possible Answers:

Correct answer:

Explanation:

 

Example Question #2 : Roots Of Polynomials

What are the roots of ?

 

Possible Answers:

Correct answer:

Explanation:

Step 1: Find two numbers that multiply to  and add 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 .

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