Factor 4x² - 25x

Factor 4x² - 25x - 99

Here we will show you how to factor the quadratic function 4x² - 25x - 99 using the box method. In other words, we will show you how to factor 4x squared minus 25x minus 99 (4x^2 - 25x - 99) using the box method. It is a 5-step process:

Step 1: The standard form of a quadratic equation is ax² + bx + c. We start by labeling the different parts of our equation 4x² - 25x - 99, like this:

a = 4
b = -25
c = -99

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

-9	-36x	-99
x	4x²	11x
	4x	11

We put 4x² (a) in the bottom left square and -99 (c) in the top right square, like this:

-9	-36x	-99
x	4x²	11x
	4x	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 4 times -99 (a × c), and add together to equal -25 (b).

More specifically, 4 times -99 is -396. Therefore, we need to find the two numbers that multiply to equal -396, and add to equal -25.

? × ? = -396
? + ? = -25

After looking at this problem, we can see that the two numbers that multiply together to equal -396, and add together to equal -25, are -36 and 11, as illustrated here:

-36 × 11 = -396
-36 + 11 = -25

Now, we can fill in the last two squares in our box with -36x and 11x. Place -36x in the upper left square, and place 11x in the lower right square.

-9	-36x	-99
x	4x²	11x
	4x	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 -36x and -99. The greatest common factor of -36x and -99 is -9. Therefore, we write -9 to the left of the top row. You can see it here in the color green:

-9	-36x	-99
x	4x²	11x
	4x	11

Next, let’s look at the bottom row. We have the terms 4x² and 11x. The greatest common factor of 4x² and 11x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

-9	-36x	-99
x	4x²	11x
	4x	11

To find the values below the table, we first divide 4x² by x (labeled in blue). This gives us 4x.

4x² ÷ x = 4x

You can see this value colored in orange below:

-9	-36x	-99
x	4x²	11x
	4x	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:

-9	-36x	-99
x	4x²	11x
	4x	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 4x² - 25x - 99. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get the answer:

(x - 9)(4x + 11)

That’s it! Now you know how to factor the equation 4x² - 25x - 99.

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