# GED Math : Solving by Factoring

## Example Questions

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### Example Question #888 : Ged Math

What is the value of  if  is a positive integer?

Explanation:

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 #21 : Quadratic Equations

. Solve for .

Explanation:

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 #22 : Quadratic Equations

Solve for :

Explanation:

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 #23 : Quadratic Equations

For what value of  will the following equation be true?

Explanation:

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 #24 : Quadratic Equations

Solve by factoring

or

or

or

Not enough information

or

Explanation:

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 #25 : Quadratic Equations

Solve for x by factoring:

or

Explanation:

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 #341 : Algebra

Factor completely:

Explanation:

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 #342 : Algebra

Find the values of x in the following:

or

No solutions

or

or

Explanation:

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 #343 : Algebra

Factor completely:

Explanation:

is in the form of  which is a perfect square binomial

***

Factor a 4 from each binomial

multiplying 4 x 4 gives the result

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