Factor -10x² - 38x

Factor -10x² - 38x - 36

Here we will show you how to factor the quadratic function -10x² - 38x - 36 using the box method. In other words, we will show you how to factor negative 10x squared minus 38x minus 36 (-10x^2 - 38x - 36) 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 + 38x + 36. Now we can label the different parts of our equation, like this:

a = 10
b = 38
c = 36

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

18	18x	36
10x	10x²	20x
	x	2

We put 10x² (a) in the bottom left square and 36 (c) in the top right square, like this:

18	18x	36
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 36 (a × c), and add together to equal 38 (b).

More specifically, 10 times 36 is 360. Therefore, we need to find the two numbers that multiply to equal 360, and add to equal 38.

? × ? = 360
? + ? = 38

After looking at this problem, we can see that the two numbers that multiply together to equal 360, and add together to equal 38, are 18 and 20, as illustrated here:

18 × 20 = 360
18 + 20 = 38

Now, we can fill in the last two squares in our box with 18x and 20x. Place 18x in the upper left square, and place 20x in the lower right square.

18	18x	36
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 18x and 36. The greatest common factor of 18x and 36 is 18. Therefore, we write 18 to the left of the top row. You can see it here in the color green:

18	18x	36
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:

18	18x	36
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:

18	18x	36
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:

18	18x	36
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 - 38x - 36. 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 + 18)(x + 2)

In our original quadratic equation, -10x² - 38x - 36, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(10x + 18)(x + 2)

That’s it! Now you know how to factor the equation -10x² - 38x - 36.

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