Factor -10x² - 40x

Factor -10x² - 40x - 40

Here we will show you how to factor the quadratic function -10x² - 40x - 40 using the box method. In other words, we will show you how to factor negative 10x squared minus 40x minus 40 (-10x^2 - 40x - 40) 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 10x² + 40x + 40. Now we can label the different parts of our equation, like this:

a = 10
b = 40
c = 40

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

20	20x	40
10x	10x²	20x
	x	2

We put 10x² (a) in the bottom left square and 40 (c) in the top right square, like this:

20	20x	40
10x	10x²	20x
	x	2

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 10 times 40 (a × c), and add together to equal 40 (b).

More specifically, 10 times 40 is 400. Therefore, we need to find the two numbers that multiply to equal 400, and add to equal 40.

? × ? = 400
? + ? = 40

After looking at this problem, we can see that the two numbers that multiply together to equal 400, and add together to equal 40, are 20 and 20, as illustrated here:

20 × 20 = 400
20 + 20 = 40

Now, we can fill in the last two squares in our box with 20x and 20x. Place 20x in the upper left square, and place 20x in the lower right square.

20	20x	40
10x	10x²	20x
	x	2

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 20x and 40. The greatest common factor of 20x and 40 is 20. Therefore, we write 20 to the left of the top row. You can see it here in the color green:

20	20x	40
10x	10x²	20x
	x	2

Next, let’s look at the bottom row. We have the terms 10x² and 20x. The greatest common factor of 10x² and 20x is 10x. Therefore, we write 10x to the left of the bottom row. You can see it here in the color blue:

20	20x	40
10x	10x²	20x
	x	2

To find the values below the table, we first divide 10x² by 10x (labeled in blue). This gives us x.

10x² ÷ 10x = x

You can see this value colored in orange below:

20	20x	40
10x	10x²	20x
	x	2

Next, we divide 20x by 10x (labeled in blue). This gives us 2.

20x ÷ 10x = 2

You can see this value colored in purple below:

20	20x	40
10x	10x²	20x
	x	2

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 -10x² - 40x - 40. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(10x + 20)(x + 2)

In our original quadratic equation, -10x² - 40x - 40, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(10x + 20)(x + 2)

That’s it! Now you know how to factor the equation -10x² - 40x - 40.

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

Factor -10x² - 40x - 30
Here is the next quadratic function on our list that we have factored for you.