# ACT Math : Binomials

## Example Questions

### Example Question #1 : How To Find The Solution To A Binomial Problem

Choose the answer below that is one of the solutions to the following equation:

Explanation:

The equation presented in the problem is:

First, you need to get everything on one side of the equation:

Then, you can reduce by dividing everything by :

Then, you factor:

Therefore,  or .

### Example Question #631 : Algebra

Choose the answer that is a potential solution to the binomial equation below:

Explanation:

The equation presented in the problem is:

To solve, first get all terms on the same side of the equation:

Now, you've eliminated your third term, which makes factoring difficult. If it makes things easier, you can throw a zero back in the equation:

Factor:

Therefore:

or

### Example Question #1 : How To Find The Solution To A Binomial Problem

Choose the answer below that is a solution to the following binomial equation:

Explanation:

First, get everything on one side of the equation:

Then, to make things easier, you can reduce by dividing everything by :

Next, factor:

Therefore:

or

### Example Question #4 : How To Find The Solution To A Binomial Problem

Choose the answer which is a solution to the following binomial equation:

Explanation:

To solve, first pull everything over to one side of the equation:

Then, reduce by dividing by the greatest common denominator—in this case, :

Now, factor:

Therefore:

or

### Example Question #5 : How To Find The Solution To A Binomial Problem

Choose the answer below that is a possible solution to the following binomial equation:

Explanation:

The equation presented in the problem is:

To solve this type of equation, you need to factor. First, get all of the terms of the equation on one side:

Then, you need to find two factors that will give you the equation in its current form:

Therefore,  and , so  or .

is listed as an answer, and must therefore be correct.

### Example Question #1 : Binomial Denominators

For the equation , what is(are) the solution(s) for ?

Explanation:

, can be factored to (x -7)(x-3) = 0. Therefore, x-7 = 0 and x-3 = 0. Solving for x in both cases, gives 7 and 3.

### Example Question #1 : Binomial Denominators

Simplify:

Explanation:

In order to begin this kind of a problem, it's key to look at parts of the rational expression that can be simplified.

In this case, the denominator is an already-simplified binomial; however, the numerator can be factored.

The roots will be numbers that sum up to  but have the product of .

The options include:

When these options are summed up:

We can negate the last three options because the first option of  and  fulfill the requirements. Therefore, the numerator can be factored into the following:

Because the quantity  appears in the denominator, this can be "canceled out." This leaves the final answer to be the quantity .

### Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Simplify:

Explanation:

In order to begin this kind of a problem, it's key to look at parts of the rational expression that can be simplified.

In this case, the denominator is an already-simplified binomial; however, the numerator can be factored through "factoring by grouping." This can be a helpful idea to keep in mind when you come across a polynomial with four terms and simplifying is involved.

can be simplified first by removing the common factor of  from the first two terms and the common factor of  from the last two terms:

This leaves two terms that are identical  and their coefficients, which can be combined into another term to complete the factoring:

Consider the denominator; the quantity  appears, so the  in the numerator and in the denominator can be cancelled out. The simplified expression is then left as .

### Example Question #51 : Variables

Solve for x when 6x – 4 = 2x + 5

3

0

9/4

1/4

9/4

Explanation:

Solve by simplifying:

6x – 4 = 2x + 5

6x = 2x + 9

4x = 9

x = 9/4

### Example Question #2 : How To Simplify Binomials

What is the value of the following equation if  and ?