Factor 99x² + 20x

Factor 99x² + 20x - 100

Here we will show you how to factor the quadratic function 99x² + 20x - 100 using the box method. In other words, we will show you how to factor 99x squared plus 20x minus 100 (99x^2 + 20x - 100) 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 99x² + 20x - 100, like this:

a = 99
b = 20
c = -100

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

-10	-90x	-100
11x	99x²	110x
	9x	10

We put 99x² (a) in the bottom left square and -100 (c) in the top right square, like this:

-10	-90x	-100
11x	99x²	110x
	9x	10

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 99 times -100 (a × c), and add together to equal 20 (b).

More specifically, 99 times -100 is -9900. Therefore, we need to find the two numbers that multiply to equal -9900, and add to equal 20.

? × ? = -9900
? + ? = 20

After looking at this problem, we can see that the two numbers that multiply together to equal -9900, and add together to equal 20, are -90 and 110, as illustrated here:

-90 × 110 = -9900
-90 + 110 = 20

Now, we can fill in the last two squares in our box with -90x and 110x. Place -90x in the upper left square, and place 110x in the lower right square.

-10	-90x	-100
11x	99x²	110x
	9x	10

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 -90x and -100. The greatest common factor of -90x and -100 is -10. Therefore, we write -10 to the left of the top row. You can see it here in the color green:

-10	-90x	-100
11x	99x²	110x
	9x	10

Next, let’s look at the bottom row. We have the terms 99x² and 110x. The greatest common factor of 99x² and 110x is 11x. Therefore, we write 11x to the left of the bottom row. You can see it here in the color blue:

-10	-90x	-100
11x	99x²	110x
	9x	10

To find the values below the table, we first divide 99x² by 11x (labeled in blue). This gives us 9x.

99x² ÷ 11x = 9x

You can see this value colored in orange below:

-10	-90x	-100
11x	99x²	110x
	9x	10

Next, we divide 110x by 11x (labeled in blue). This gives us 10.

110x ÷ 11x = 10

You can see this value colored in purple below:

-10	-90x	-100
11x	99x²	110x
	9x	10

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 99x² + 20x - 100. 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:

(11x - 10)(9x + 10)

That’s it! Now you know how to factor the equation 99x² + 20x - 100.

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