Factor -100x² - 95x

Factor -100x² - 95x - 12

Here we will show you how to factor the quadratic function -100x² - 95x - 12 using the box method. In other words, we will show you how to factor negative 100x squared minus 95x minus 12 (-100x^2 - 95x - 12) 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 100x² + 95x + 12. Now we can label the different parts of our equation, like this:

a = 100
b = 95
c = 12

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

3	15x	12
20x	100x²	80x
	5x	4

We put 100x² (a) in the bottom left square and 12 (c) in the top right square, like this:

3	15x	12
20x	100x²	80x
	5x	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 100 times 12 (a × c), and add together to equal 95 (b).

More specifically, 100 times 12 is 1200. Therefore, we need to find the two numbers that multiply to equal 1200, and add to equal 95.

? × ? = 1200
? + ? = 95

After looking at this problem, we can see that the two numbers that multiply together to equal 1200, and add together to equal 95, are 15 and 80, as illustrated here:

15 × 80 = 1200
15 + 80 = 95

Now, we can fill in the last two squares in our box with 15x and 80x. Place 15x in the upper left square, and place 80x in the lower right square.

3	15x	12
20x	100x²	80x
	5x	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 15x and 12. The greatest common factor of 15x and 12 is 3. Therefore, we write 3 to the left of the top row. You can see it here in the color green:

3	15x	12
20x	100x²	80x
	5x	4

Next, let’s look at the bottom row. We have the terms 100x² and 80x. The greatest common factor of 100x² and 80x is 20x. Therefore, we write 20x to the left of the bottom row. You can see it here in the color blue:

3	15x	12
20x	100x²	80x
	5x	4

To find the values below the table, we first divide 100x² by 20x (labeled in blue). This gives us 5x.

100x² ÷ 20x = 5x

You can see this value colored in orange below:

3	15x	12
20x	100x²	80x
	5x	4

Next, we divide 80x by 20x (labeled in blue). This gives us 4.

80x ÷ 20x = 4

You can see this value colored in purple below:

3	15x	12
20x	100x²	80x
	5x	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 -100x² - 95x - 12. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(20x + 3)(5x + 4)

In our original quadratic equation, -100x² - 95x - 12, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(20x + 3)(5x + 4)

That’s it! Now you know how to factor the equation -100x² - 95x - 12.

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