ACT Math : How to factor a trinomial

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Factor A Trinomial

Find the -intercepts:

Possible Answers:

 and 

 only

 and 

 and 

Correct answer:

 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 .

Possible Answers:

Correct answer:

Explanation:

1. Factor the expression:

 

2. Solve for :

and...

Example Question #3 : Trinomials

Factor the following expression:

Possible Answers:

Correct answer:

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 #4 : Trinomials

Factor the expression completely

Possible Answers:

Correct answer:

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 #71 : Variables

Which expression is equivalent to the polynomial .

Possible Answers:

Correct answer:

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 #2 : How To Factor A Trinomial

Which expression is equivalent to the following polynomial: 

Possible Answers:

Correct answer:

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 #73 : Variables

Which expression is equivalent to the following polynomial: 

Possible Answers:

Correct answer:

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  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.

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