# ACT Math : How to factor a variable

## Example Questions

### Example Question #1 : Factoring

Two consecutive positive multiples of five have a product of 300. What is their sum?

15

20

25

35

45

35

Explanation:

Define the variables as x = 1st number and x + 5 = 2nd number, so the product is given as x(x + 5) = 300, which becomes x2 + 5x – 300 = 0.

Factoring results in (x + 20)(x – 15) = 0, so the positive answer is 15, making the second number 20.

The sum of the two numbers is 35.

### Example Question #2 : Factoring

Factor 12x3y+ 156x2y3

x2y3(xy + 13)

12x2y3(xy + 13)

12x2y3

12xy(xy + 13)

12x2y3(xy + 13)

Explanation:

The common factors are 12, x2, and y3.

So 12x2y3(xy + 13)

### Example Question #1 : How To Factor A Variable

Solve for all solutions of :

Explanation:

First move all of the variables to the left side of the equation. Combine similar terms, and set the equation equal to zero. Then factor the equation to get

Thus the solutions of  are 4 and 6.

### Example Question #3 : Factoring

Simplify:

Explanation:

factors to

One  cancels from the bottom, leaving

### Example Question #1 : Factoring

Factor:

Explanation:

In the form of  you must find two numbers which add to give you  and multiply to give you  and then put them in the form of ( + number) ( + number)

To check, multiply the two expressions out and it should equal

### Example Question #4 : Factoring

Factor the following expression:

The expression is already simplified as much as possible.

Explanation:

To factor an expression we look for the greatest common factor.

Remember that

Thus:

### Example Question #5 : Factoring

Factor the following expression: