Factoring Trinomials Practice Problems Answers

 

1. 2x² + 7x + 3 factors into (2x + 1)(x + 3).
2. 3x² + 10x + 7 factors into (3x + 7)(x + 1).
3. 4x² + 12x + 9 factors into (2x + 3)(2x + 3) or (2x + 3)².
4. 5x² + 11x - 6 does not factor.
5. 6x² + 13x - 5 factors into (3x - 1)(2x + 5).
6. 7x² + 20x + 12 does not factor.
7. 8x² + 15x - 9 does not factor.
8. 9x² + 8x - 1 factors into (9x - 1)(x + 1).
9. 10x² + 23x + 12 factors into (2x + 3)(5x + 4).
10. 11x² + 26x + 15 factors into (11x + 15)(x + 1).
11. 12x² + 18x - 24 factors into 6(x² + 3x - 4).
12. 13x² + 7x - 10 does not factor.
13. 14x² + 17x - 6 factors into (2x + 3)(7x - 2).
14. 15x² + 29x + 14 factors into (5x + 2)(3x + 7).
15. 16x² + 8x - 10 factors into 2(8x² + 4x - 5)
16. 17x² + 13x - 30 does not factor
17. 18x² + 16x + 4 factors into 2(9x² + 8x + 2)
18. 19x² + 25x + 6 factors into (19x + 6)(x + 1).
19. 20x² + 14x - 24 does not factor.
20. 21x² + 20x - 4 does not factor.

Factoring Trinomials Practice Problems

 A very important skill a math student should have, is the ability to factor trinomials quickly.

Here are twenty to practice on.

1. 2x² + 7x + 3
2. 3x² + 10x + 7
3. 4x² + 12x + 9
4. 5x² + 11x - 6
5. 6x² + 13x - 5
6. 7x² + 20x + 12
7. 8x² + 15x - 9
8. 9x² + 8x - 1
9. 10x² + 23x + 12
10. 11x² + 26x + 15
11. 12x² + 18x - 24
12. 13x² + 7x - 10
13. 14x² + 17x - 6
14. 15x² + 29x + 14
15. 16x² + 8x - 10
16. 17x² + 13x - 30
17. 18x² + 16x + 4
18. 19x² + 25x + 6
19. 20x² + 14x - 24
20. 21x² + 20x - 4

Choosing the right method to solve a word problem

 As you have seen, there are many ways to solve this word problem.  Now, some word problem or systems of equations will make it easier to solve a certain way than others.

Examples:

2x+5y = 12

3x-5y = -7

Elimination would be easiest because you can just add the two equations and immediately get rid of the y variable.

Whereas a problem like this:

x=2y-1

2x+7y=9 

Would be best solved by substitution since it is already solved for x.  Now, just put that in the 2nd equation.

This problem 

7x-5y=2

13x-7y=6

would work very well with Cramer's rule.

While this problem:

3.457x-9.28y=23.87

4.672x+12.82345y=-1.0023

I would jump right on one of the websites I mentioned!  I wouldn't waste my time with any of the other methods.  Yes, it is fine to use a calculator or website to solve problems but you shouldn't use them for easier problems.  

A problem like:

x+3y=4

2x-5y=-3

Would be great with gaussian elimination.  

So, knowing many methods will be very helpful to solving problems quickly and accurately.

Remember, if you need help, contact me.  I have VERY affordable rates.

7th Solving the problem using websites

I am showing you many ways to solve the same word problem.  In this post we will use 3 Websites to solve it. 

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

We will use x for the number of students and y for the number of adults.

The three websites I used were:

desmos.com

wolframalpha.com

symbolab.com

Please watch the video to see how to do it.

6th Solving the problem using Matrix Inverses

 I am showing you many ways to solve the same word problem.  In this post we will use Matrix Inverses to solve it.  I do NOT recommend this way to solve a 2x2.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

We will use x for the number of students and y for the number of adults.

Please watch the video to see how to do it.

5th Solving the problem using Cramer's Rule

I am showing you many ways to solve the same word problem.  In this post we will use Cramer's Rule to solve it.  This is my favorite way to solve 2x2s.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

We will use x for the number of students and y for the number of adults.

Please watch the video to see how to do it.

4th Solving the problem using gaussian elimination (also called row reduction)

  I am showing you many ways to solve the same word problem.  In this post we will use gaussian elimination (also called row reduction) to solve it.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

We will use x for the number of students and y for the number of adults.

Please watch the video to see how to do it.

3rd Solving the problem using elimination

 I am showing you many ways to solve the same word problem.  In this post we will use elimination to solve it.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

We will use x for the number of students and y for the number of adults.

Please watch the video to see how to do it.

NOTE:  You will notice I made a couple mistakes.  I left those mistakes in for a couple reasons.

• To show you that everyone makes mistakes, so don't worry about it if you make a mistake.
• To emphasize the importance of being able to ask yourself "does my answer make sense" and then make the decision.

2nd Solving the problem using substitution.

I am showing you many ways to solve the same word problem.  In this post we will use substitution to solve it.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

We will use x for the number of students and y for the number of adults.

Please watch the video to see how to do it.

1st Solving the problem using only a single variable.

 Over the next few posts, I will show you many ways to solve the same word problem.  In this video, I will show you how to solve the problem using only a single variable.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

For this problem we are going to use x for the number of students and 100-x for the number of adults.

Watch the video to make sure you understand how to do the problem.

Solving a word problem using single and multiple variables.

Over the next few posts, I will show you many ways to solve the same word problem.

Here is the word problem:

You and some friends are going to the movies.  They charge $9 for adults and $7 for children.  The movie theatre had 100 customers and made $790 that night.  How many of each type of ticket did they sell?

First, when working on a word problem you should ALWAYS do a setup. In this setup you explain what the variables that you are using stand for.

Examples:

t = time in seconds since program started

t = time in years since 1900

x = number of students in the class

I have seen so many students do good work but then get the answer wrong because they didn't do a setup and make sure the answer they got was what they were looking for.  So, please pay careful attention to the setup in the following posts and learn how to do it well.