### All ACT Math Resources

## Example Questions

### 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 #1 : Trinomials

Solve for when .

**Possible Answers:**

**Correct answer:**

1. Factor the expression:

2. Solve for :

and...

### Example Question #61 : Variables

Factor the following expression:

**Possible Answers:**

**Correct answer:**

Remember that when you factor a trinomial in the form , you need to find factors of that add up to .

First, write down all the possible factors of .

Then add them to see which one gives you the value of

Thus, the factored form of the expression is

### Example Question #4 : How To Factor A Trinomial

Factor the expression completely

**Possible Answers:**

**Correct answer:**

First, find any common factors. In this case, there is a common factor:

Now, factor the trinomial.

To factor the trinomial, you will need to find factors of that add up to .

List out the factors of , then add them.

Thus,

### Example Question #651 : Algebra

Which expression is equivalent to the polynomial .

**Possible Answers:**

**Correct answer:**

This question calls for us to factor the polynomial into two binomials. Since the first term is and the last term is a number without a variable, we know that how answer will be of the form where a and b are positive or negative numbers.

To find a and b we look at the second and third term. Since the second term is we know . (The x comes from a and b multiplying by x and then adding with each other). The +10 term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & -10 and -1 & 10 are the possible pairs. Now we can look and see which one adds up to make 9. This gives us the pair -1 & 10 and we plug that into the equation as a and b to get our final answer.

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

Which expression is equivalent to the following polynomial:

**Possible Answers:**

**Correct answer:**

This question calls for us to factor the polynomial into two binomials. Since the first term is and the last term is a number without a variable, we know that how answer will be of the form where a and b are positive or negative numbers.

To find a and b we look at the second and third term. Since the second term is we know . (The x comes from a and b multiplying by x and then adding with each other). The -14 term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & -14, 2 & -7, -2 & 7, and -1 & 14 are the possible pairs. Now we can look and see which one adds up to make 5. This gives us the pair -2 & 7 and we plug that into the equation as a and b to get our final answer.

### Example Question #7 : How To Factor A Trinomial

Which expression is equivalent to the following polynomial:

**Possible Answers:**

**Correct answer:**

This question calls for us to factor the polynomial into two binomials. Since the first term is and the last term is a number without a variable, we know that how answer will be of the form where a and b are positive or negative numbers.

To find a and b we look at the second and third term. Since the second term is we know . (The x comes from a and b multiplying by x and then adding with each other). The term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & 8, 2 & 4, -2 & -4, and -1 & -8 are the possible pairs. Now we can look and see which one adds up to make -9. This gives us the pair -1 & -8 and we plug that into the equation as a and b to get our final answer.

### Example Question #71 : Variables

Simplify the following:

**Possible Answers:**

**Correct answer:**

To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.

Now we treat this as the addition of three monomials multiplied by a trinomial.

Now combine like terms and order by degree, largest to smallest.

### Example Question #2 : How To Multiply Trinomials

Solve:

**Possible Answers:**

**Correct answer:**

The is distributed and multiplied to each term , , and .

### Example Question #3 : How To Multiply Trinomials

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

is multiplied to both and and is only multiplied to .

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