# ACT Math : Polynomials

## Example Questions

### Example Question #1 : Binomials And Foil

Which of the following expressions is equivalent to: 6x (m2 +yx2 3)?

6xm2 + 6yx2 -18x

6xm2 + 6yx3 -18x

6xm2 + 7x3 -18

6xm2 + 6yx3 -18

xm2 + 7x3 -18

6xm2 + 6yx3 -18x

Explanation:

6x (m2 +yx2 3)= 6x∙m2 + 6xyx2 – 6x∙3= 6xm2 + 6yx3 -18x (Use Distributive Property)

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

Which of the following expressions is equivalent to: ?

Explanation:

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 ?

Cannot be determined from the given information.

Explanation:

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 ?

Explanation:

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 ?

Explanation:

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 ?

Explanation:

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 ?

Explanation:

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 #7 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

Explanation:

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 : Trinomials

Find the -intercepts:

and

and

only

and

and

Explanation:

-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 .