Factor -2x² - 21x

Factor -2x² - 21x - 55

Here we will show you how to factor the quadratic function -2x² - 21x - 55 using the box method. In other words, we will show you how to factor negative 2x squared minus 21x minus 55 (-2x^2 - 21x - 55) 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 2x² + 21x + 55. Now we can label the different parts of our equation, like this:

a = 2
b = 21
c = 55

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

5	10x	55
x	2x²	11x
	2x	11

We put 2x² (a) in the bottom left square and 55 (c) in the top right square, like this:

5	10x	55
x	2x²	11x
	2x	11

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 2 times 55 (a × c), and add together to equal 21 (b).

More specifically, 2 times 55 is 110. Therefore, we need to find the two numbers that multiply to equal 110, and add to equal 21.

? × ? = 110
? + ? = 21

After looking at this problem, we can see that the two numbers that multiply together to equal 110, and add together to equal 21, are 10 and 11, as illustrated here:

10 × 11 = 110
10 + 11 = 21

Now, we can fill in the last two squares in our box with 10x and 11x. Place 10x in the upper left square, and place 11x in the lower right square.

5	10x	55
x	2x²	11x
	2x	11

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 10x and 55. The greatest common factor of 10x and 55 is 5. Therefore, we write 5 to the left of the top row. You can see it here in the color green:

5	10x	55
x	2x²	11x
	2x	11

Next, let’s look at the bottom row. We have the terms 2x² and 11x. The greatest common factor of 2x² and 11x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

5	10x	55
x	2x²	11x
	2x	11

To find the values below the table, we first divide 2x² by x (labeled in blue). This gives us 2x.

2x² ÷ x = 2x

You can see this value colored in orange below:

5	10x	55
x	2x²	11x
	2x	11

Next, we divide 11x by x (labeled in blue). This gives us 11.

11x ÷ x = 11

You can see this value colored in purple below:

5	10x	55
x	2x²	11x
	2x	11

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 -2x² - 21x - 55. 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 + 5)(2x + 11)

In our original quadratic equation, -2x² - 21x - 55, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(x + 5)(2x + 11)

That’s it! Now you know how to factor the equation -2x² - 21x - 55.

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Factor -2x² - 21x - 54
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