Factor -7x² - 39x

Factor -7x² - 39x - 44

Here we will show you how to factor the quadratic function -7x² - 39x - 44 using the box method. In other words, we will show you how to factor negative 7x squared minus 39x minus 44 (-7x^2 - 39x - 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 + 39x + 44. Now we can label the different parts of our equation, like this:

a = 7
b = 39
c = 44

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

11	11x	44
7x	7x²	28x
	x	4

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

11	11x	44
7x	7x²	28x
	x	4

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 39 (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 39.

? × ? = 308
? + ? = 39

After looking at this problem, we can see that the two numbers that multiply together to equal 308, and add together to equal 39, are 11 and 28, as illustrated here:

11 × 28 = 308
11 + 28 = 39

Now, we can fill in the last two squares in our box with 11x and 28x. Place 11x in the upper left square, and place 28x in the lower right square.

11	11x	44
7x	7x²	28x
	x	4

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 11x and 44. The greatest common factor of 11x and 44 is 11. Therefore, we write 11 to the left of the top row. You can see it here in the color green:

11	11x	44
7x	7x²	28x
	x	4

Next, let’s look at the bottom row. We have the terms 7x² and 28x. The greatest common factor of 7x² and 28x is 7x. Therefore, we write 7x to the left of the bottom row. You can see it here in the color blue:

11	11x	44
7x	7x²	28x
	x	4

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

7x² ÷ 7x = x

You can see this value colored in orange below:

11	11x	44
7x	7x²	28x
	x	4

Next, we divide 28x by 7x (labeled in blue). This gives us 4.

28x ÷ 7x = 4

You can see this value colored in purple below:

11	11x	44
7x	7x²	28x
	x	4

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 - 39x - 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:

(7x + 11)(x + 4)

In our original quadratic equation, -7x² - 39x - 44, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(7x + 11)(x + 4)

That’s it! Now you know how to factor the equation -7x² - 39x - 44.

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