Factor 3x² - 13x - 100


Factoring Quadratics

Here we will show you how to factor the quadratic function 3x² - 13x - 100 using the box method. In other words, we will show you how to factor 3x squared minus 13x minus 100 (3x^2 - 13x - 100) using the box method. It is a 5-step process:

Step 1: The standard form of a quadratic equation is ax² + bx + c. We start by labeling the different parts of our equation 3x² - 13x - 100, like this:

a = 3
b = -13
c = -100


Step 2: Next, we need to draw a box and divide it into four squares:

-25  -25x -100
3x  3x² 12x
x 4
We put 3x² (a) in the bottom left square and -100 (c) in the top right square, like this:

-25  -25x -100
3x  3x² 12x
x 4
Step 3: In order to fill in the other two squares, we need to do some math. We have to find two numbers that multiply together to give us the product of 3 times -100 (a × c), and add together to equal -13 (b).

More specifically, 3 times -100 is -300. Therefore, we need to find the two numbers that multiply to equal -300, and add to equal -13.

? × ? = -300
? + ? = -13

After looking at this problem, we can see that the two numbers that multiply together to equal -300, and add together to equal -13, are -25 and 12, as illustrated here:

-25 × 12 = -300
-25 + 12 = -13

Now, we can fill in the last two squares in our box with -25x and 12x. Place -25x in the upper left square, and place 12x in the lower right square.

-25  -25x -100
3x  3x² 12x
x 4
Step 4: Next, we need to find four final numbers to finish factoring our equation. We can see that our box is a 2 x 2 table made up of rows and columns.

Our goal is to find the numbers that, when multiplied together, result in the products in each square. We can do this by finding the greatest common factor in each row.

Let’s look at the top row. We have the terms -25x and -100. The greatest common factor of -25x and -100 is -25. Therefore, we write -25 to the left of the top row. You can see it here in the color green:

-25  -25x -100
3x  3x² 12x
x 4
Next, let’s look at the bottom row. We have the terms 3x² and 12x. The greatest common factor of 3x² and 12x is 3x. Therefore, we write 3x to the left of the bottom row. You can see it here in the color blue:

-25  -25x -100
3x  3x² 12x
x 4
To find the values below the table, we first divide 3x² by 3x (labeled in blue). This gives us x.

3x² ÷ 3x = x

You can see this value colored in orange below:

-25  -25x -100
3x  3x² 12x
x 4

Next, we divide 12x by 3x (labeled in blue). This gives us 4.

12x ÷ 3x = 4

You can see this value colored in purple below:

-25  -25x -100
3x  3x² 12x
x 4

Step 5: Now we have all of the information we need to finish factoring the equation. The values outside of the box are used to factor 3x² - 13x - 100. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get the answer:

(3x - 25)(x + 4)

That’s it! Now you know how to factor the equation 3x² - 13x - 100.


Factoring Quadratics
Go here if you want to learn how to factor another quadratic function.

Factor 3x² - 13x - 88
Here is the next quadratic function on our list that we have factored for you.


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