Factor -28x² - 20x

Factor -28x² - 20x - 3

Here we will show you how to factor the quadratic function -28x² - 20x - 3 using the box method. In other words, we will show you how to factor negative 28x squared minus 20x minus 3 (-28x^2 - 20x - 3) 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 28x² + 20x + 3. Now we can label the different parts of our equation, like this:

a = 28
b = 20
c = 3

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

3	6x	3
14x	28x²	14x
	2x	1

We put 28x² (a) in the bottom left square and 3 (c) in the top right square, like this:

3	6x	3
14x	28x²	14x
	2x	1

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 28 times 3 (a × c), and add together to equal 20 (b).

More specifically, 28 times 3 is 84. Therefore, we need to find the two numbers that multiply to equal 84, and add to equal 20.

? × ? = 84
? + ? = 20

After looking at this problem, we can see that the two numbers that multiply together to equal 84, and add together to equal 20, are 6 and 14, as illustrated here:

6 × 14 = 84
6 + 14 = 20

Now, we can fill in the last two squares in our box with 6x and 14x. Place 6x in the upper left square, and place 14x in the lower right square.

3	6x	3
14x	28x²	14x
	2x	1

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 6x and 3. The greatest common factor of 6x and 3 is 3. Therefore, we write 3 to the left of the top row. You can see it here in the color green:

3	6x	3
14x	28x²	14x
	2x	1

Next, let’s look at the bottom row. We have the terms 28x² and 14x. The greatest common factor of 28x² and 14x is 14x. Therefore, we write 14x to the left of the bottom row. You can see it here in the color blue:

3	6x	3
14x	28x²	14x
	2x	1

To find the values below the table, we first divide 28x² by 14x (labeled in blue). This gives us 2x.

28x² ÷ 14x = 2x

You can see this value colored in orange below:

3	6x	3
14x	28x²	14x
	2x	1

Next, we divide 14x by 14x (labeled in blue). This gives us 1.

14x ÷ 14x = 1

You can see this value colored in purple below:

3	6x	3
14x	28x²	14x
	2x	1

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 -28x² - 20x - 3. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(14x + 3)(2x + 1)

In our original quadratic equation, -28x² - 20x - 3, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(14x + 3)(2x + 1)

That’s it! Now you know how to factor the equation -28x² - 20x - 3.

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