### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Roots Of Polynomials

What are the roots of the polynomial: ?

**Possible Answers:**

None of the Above

**Correct answer:**

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 : Algebra

Solve for :

**Possible Answers:**

**Correct answer:**

Step 1: Factor by pairs:

Step 2: Re-write the factorization:

Step 3: Solve for x:

### Example Question #1 : Algebra

Find :

**Possible Answers:**

No Solutions Exist

**Correct answer:**

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 #1 : Algebra

**Possible Answers:**

**Correct answer:**

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 : Polynomials

Find all of the roots for the polynomial below:

**Possible Answers:**

**Correct answer:**

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 : Algebra

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Polynomials

What are the roots of ?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #1 : Classifying Algebraic Functions

Find all of the roots for the polynomial below:

**Possible Answers:**

**Correct answer:**

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: .

**Possible Answers:**

**Correct answer:**

Step 1: Evaluate .

Step 2. Evaluate

From the previous step, we already know what is.

is just multiplying by another

Step 3: Evaluate .

The expansion of is

### Example Question #1 : Binomial Expansion

What is the expansion of ?

**Possible Answers:**

**Correct answer:**

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 term and end with a constant.

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:

. This is the solution.

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