Factor -4x² - 28x

Factor -4x² - 28x - 33

Here we will show you how to factor the quadratic function -4x² - 28x - 33 using the box method. In other words, we will show you how to factor negative 4x squared minus 28x minus 33 (-4x^2 - 28x - 33) using the box method. It is a 5-step process:

Step 1: The standard form of a quadratic equation is ax² + bx + c. In this equation, a is negative. Therefore, we need to start by setting aside the negative (-). We do this by flipping the signs in the equation to get 4x² + 28x + 33. Now we can label the different parts of our equation, like this:

a = 4
b = 28
c = 33

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

3	6x	33
2x	4x²	22x
	2x	11

We put 4x² (a) in the bottom left square and 33 (c) in the top right square, like this:

3	6x	33
2x	4x²	22x
	2x	11

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 4 times 33 (a × c), and add together to equal 28 (b).

More specifically, 4 times 33 is 132. Therefore, we need to find the two numbers that multiply to equal 132, and add to equal 28.

? × ? = 132
? + ? = 28

After looking at this problem, we can see that the two numbers that multiply together to equal 132, and add together to equal 28, are 6 and 22, as illustrated here:

6 × 22 = 132
6 + 22 = 28

Now, we can fill in the last two squares in our box with 6x and 22x. Place 6x in the upper left square, and place 22x in the lower right square.

3	6x	33
2x	4x²	22x
	2x	11

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 6x and 33. The greatest common factor of 6x and 33 is 3. Therefore, we write 3 to the left of the top row. You can see it here in the color green:

3	6x	33
2x	4x²	22x
	2x	11

Next, let’s look at the bottom row. We have the terms 4x² and 22x. The greatest common factor of 4x² and 22x is 2x. Therefore, we write 2x to the left of the bottom row. You can see it here in the color blue:

3	6x	33
2x	4x²	22x
	2x	11

To find the values below the table, we first divide 4x² by 2x (labeled in blue). This gives us 2x.

4x² ÷ 2x = 2x

You can see this value colored in orange below:

3	6x	33
2x	4x²	22x
	2x	11

Next, we divide 22x by 2x (labeled in blue). This gives us 11.

22x ÷ 2x = 11

You can see this value colored in purple below:

3	6x	33
2x	4x²	22x
	2x	11

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 -4x² - 28x - 33. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(2x + 3)(2x + 11)

In our original quadratic equation, -4x² - 28x - 33, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(2x + 3)(2x + 11)

That’s it! Now you know how to factor the equation -4x² - 28x - 33.

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

Factor -4x² - 28x - 24
Here is the next quadratic function on our list that we have factored for you.