Factor -7x² - 36x

Factor -7x² - 36x - 44

Here we will show you how to factor the quadratic function -7x² - 36x - 44 using the box method. In other words, we will show you how to factor negative 7x squared minus 36x minus 44 (-7x^2 - 36x - 44) 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 7x² + 36x + 44. Now we can label the different parts of our equation, like this:

a = 7
b = 36
c = 44

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

2	14x	44
x	7x²	22x
	7x	22

We put 7x² (a) in the bottom left square and 44 (c) in the top right square, like this:

2	14x	44
x	7x²	22x
	7x	22

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 7 times 44 (a × c), and add together to equal 36 (b).

More specifically, 7 times 44 is 308. Therefore, we need to find the two numbers that multiply to equal 308, and add to equal 36.

? × ? = 308
? + ? = 36

After looking at this problem, we can see that the two numbers that multiply together to equal 308, and add together to equal 36, are 14 and 22, as illustrated here:

14 × 22 = 308
14 + 22 = 36

Now, we can fill in the last two squares in our box with 14x and 22x. Place 14x in the upper left square, and place 22x in the lower right square.

2	14x	44
x	7x²	22x
	7x	22

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 14x and 44. The greatest common factor of 14x and 44 is 2. Therefore, we write 2 to the left of the top row. You can see it here in the color green:

2	14x	44
x	7x²	22x
	7x	22

Next, let’s look at the bottom row. We have the terms 7x² and 22x. The greatest common factor of 7x² and 22x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

2	14x	44
x	7x²	22x
	7x	22

To find the values below the table, we first divide 7x² by x (labeled in blue). This gives us 7x.

7x² ÷ x = 7x

You can see this value colored in orange below:

2	14x	44
x	7x²	22x
	7x	22

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

22x ÷ x = 22

You can see this value colored in purple below:

2	14x	44
x	7x²	22x
	7x	22

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 -7x² - 36x - 44. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(x + 2)(7x + 22)

In our original quadratic equation, -7x² - 36x - 44, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(x + 2)(7x + 22)

That’s it! Now you know how to factor the equation -7x² - 36x - 44.

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