### All ACT Math Resources

## Example Questions

### Example Question #1 : Binomials And Foil

Which of the following expressions is equivalent to: 6x (m^{2 }+yx^{2 }*–*3)?

**Possible Answers:**

6xm^{2} + 6yx^{2} -18x

6xm^{2} + 6yx^{3} -18x

6xm^{2} + 7x^{3} -18

6xm^{2} + 6yx^{3} -18

xm^{2} + 7x^{3} -18

**Correct answer:**

6xm^{2} + 6yx^{3} -18x

6x (m^{2 }+yx^{2 }*–*3)= 6x∙m^{2 }+ 6xyx^{2} – 6x∙3= 6xm^{2} + 6yx^{3 }-18x (Use Distributive Property)

### Example Question #1 : How To Multiply Binomials With The Distributive Property

Which of the following expressions is equivalent to: ?

**Possible Answers:**

**Correct answer:**

Use the distributive property to multiply by all of the terms in :

### Example Question #2 : How To Multiply Binomials With The Distributive Property

If and are constants and is equivalent to , what is the value of ?

**Possible Answers:**

Cannot be determined from the given information.

**Correct answer:**

The question gives us a quadratic expression and its factored form. From this, we know

At this point, solve for t.

Now, we can plug in to get

.

Now, use FOIL to get s.

### Example Question #3 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

### Example Question #4 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

### Example Question #5 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

### Example Question #1 : Binomials And Foil

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

### Example Question #7 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Trinomials

Find the -intercepts:

**Possible Answers:**

and

and

only

and

**Correct answer:**

and

-intercepts occur when .

1. Set the expression equal to and rearrange:

2. Factor the expression:

3. Solve for :

and...

4. Rewrite the answers as coordinates:

becomes and becomes .

### Example Question #2 : How To Factor A Trinomial

Solve for when .

**Possible Answers:**

**Correct answer:**

1. Factor the expression:

2. Solve for :

and...

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