# ACT Math : How to factor a trinomial

## Example Questions

### Example Question #1 : Trinomials

Find the -intercepts:

and

only

and

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 : Trinomials

Solve for  when .

Explanation:

1. Factor the expression:

2. Solve for :

and...

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

Factor the following expression:

Explanation:

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 #1 : How To Factor A Trinomial

Factor the expression completely

Explanation:

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 #5 : Trinomials

Which expression is equivalent to the polynomial .

Explanation:

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 #6 : Trinomials

Which expression is equivalent to the following polynomial:

Explanation:

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 #71 : Variables

Which expression is equivalent to the following polynomial: