Factor -15x² - 55x + 70

Here we will show you how to factor the quadratic function -15x² - 55x + 70 using the box method. In other words, we will show you how to factor negative 15x squared minus 55x plus 70 (-15x^2 - 55x + 70) 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 15x² + 55x - 70. Now we can label the different parts of our equation, like this:

a = 15
b = 55
c = -70

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

-5	-15x	-70
5x	15x²	70x
	3x	14

We put 15x² (a) in the bottom left square and -70 (c) in the top right square, like this:

-5	-15x	-70
5x	15x²	70x
	3x	14

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 15 times -70 (a × c), and add together to equal 55 (b).

More specifically, 15 times -70 is -1050. Therefore, we need to find the two numbers that multiply to equal -1050, and add to equal 55.

? × ? = -1050
? + ? = 55

After looking at this problem, we can see that the two numbers that multiply together to equal -1050, and add together to equal 55, are -15 and 70, as illustrated here:

-15 × 70 = -1050
-15 + 70 = 55

Now, we can fill in the last two squares in our box with -15x and 70x. Place -15x in the upper left square, and place 70x in the lower right square.

-5	-15x	-70
5x	15x²	70x
	3x	14

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 -15x and -70. The greatest common factor of -15x and -70 is -5. Therefore, we write -5 to the left of the top row. You can see it here in the color green:

-5	-15x	-70
5x	15x²	70x
	3x	14

Next, let’s look at the bottom row. We have the terms 15x² and 70x. The greatest common factor of 15x² and 70x is 5x. Therefore, we write 5x to the left of the bottom row. You can see it here in the color blue:

-5	-15x	-70
5x	15x²	70x
	3x	14

To find the values below the table, we first divide 15x² by 5x (labeled in blue). This gives us 3x.

15x² ÷ 5x = 3x

You can see this value colored in orange below:

-5	-15x	-70
5x	15x²	70x
	3x	14

Next, we divide 70x by 5x (labeled in blue). This gives us 14.

70x ÷ 5x = 14

You can see this value colored in purple below:

-5	-15x	-70
5x	15x²	70x
	3x	14

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 -15x² - 55x + 70. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(5x - 5)(3x + 14)

In our original quadratic equation, -15x² - 55x + 70, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(5x - 5)(3x + 14)

That’s it! Now you know how to factor the equation -15x² - 55x + 70.

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

Factor -15x² - 55x + 100
Here is the next quadratic function on our list that we have factored for you.