### All GED Math Resources

## Example Questions

### Example Question #21 : Solving By Factoring

What is the value of if is a positive integer?

**Possible Answers:**

**Correct answer:**

Start by factoring the equation.

We will need two numbers that multiply up to and add up to . These two numbers are .

Thus, we can factor the equation.

Solving the equation will give the following solutions:

and

Since the question states that must be a positive integer, can only equal to .

### Example Question #22 : Solving By Factoring

. Solve for .

**Possible Answers:**

**Correct answer:**

In order to solve this equation, you need to factor the expression,

.

To do so, you need to find two factors of that have a sum of .

The two factors are and and the correct factoring is

,

so you know that

.

Therefore, will be equal to any values that give the inside of the parentheses a value of .

So, is equal to both and .

### Example Question #23 : Solving By Factoring

Solve for :

**Possible Answers:**

**Correct answer:**

Start by factoring the equation:

For this equation, we will want two numbers that add up to and multiply up to . In this case, the two numbers are and .

We can then write the following:

Now, set each factor equal to zero and solve for .

and

### Example Question #24 : Solving By Factoring

For what value of will the following equation be true?

**Possible Answers:**

**Correct answer:**

Start by factoring . Since one factor is already given to you, you just need to figure out what number when multiplied by will give and when added to will give . The only number that fits both criteria is . must be equal to .

### Example Question #25 : Solving By Factoring

Solve by factoring

**Possible Answers:**

or

Not enough information

or

or

**Correct answer:**

or

We must start by factoring

We must think of two numbers that multiply to be 15 and add to be 8. We come up with 3 and 5

Then

So we have

Which means either or

So, or

### Example Question #26 : Solving By Factoring

Solve for x by factoring:

**Possible Answers:**

or

**Correct answer:**

Looking at , we notice that it is a perfect square trinomial.

*A perfect square trinomial is given by the form (where "a" represents a variable term and "b" represents a constant term).

*Comparing this to our trinomial, we find...

*So, we confirm it is, indeed, a perfect square trinomial.

We have one solution:

### Example Question #26 : Solving By Factoring

Factor completely:

**Possible Answers:**

**Correct answer:**

1) First to note in this problem is a common factor of in

2) Factoring an , we have

3) We now have and a factorable trinomial.

4)

5) Two numbers that add to 2 and have a product of -48 are: 8 and -6

6)

### Example Question #28 : Solving By Factoring

Find the values of x in the following:

**Possible Answers:**

or

or

No solutions

**Correct answer:**

or

This question can be answered by factoring

Our factors will be in the form

We need to find and such that and

We notice that and fit those criteria

Then:

We need to consider both binomials can equal 0 and satisfy the equation

### Example Question #27 : Solving By Factoring

Factor completely:

**Possible Answers:**

**Correct answer:**

is in the form of which is a perfect square binomial

***

Factor a 4 from each binomial

multiplying 4 x 4 gives the result