Factor 99x² - 98x

Factor 99x² - 98x - 85

Here we will show you how to factor the quadratic function 99x² - 98x - 85 using the box method. In other words, we will show you how to factor 99x squared minus 98x minus 85 (99x^2 - 98x - 85) 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 - 98x - 85, like this:

a = 99
b = -98
c = -85

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

-17	-153x	-85
11x	99x²	55x
	9x	5

We put 99x² (a) in the bottom left square and -85 (c) in the top right square, like this:

-17	-153x	-85
11x	99x²	55x
	9x	5

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 -85 (a × c), and add together to equal -98 (b).

More specifically, 99 times -85 is -8415. Therefore, we need to find the two numbers that multiply to equal -8415, and add to equal -98.

? × ? = -8415
? + ? = -98

After looking at this problem, we can see that the two numbers that multiply together to equal -8415, and add together to equal -98, are -153 and 55, as illustrated here:

-153 × 55 = -8415
-153 + 55 = -98

Now, we can fill in the last two squares in our box with -153x and 55x. Place -153x in the upper left square, and place 55x in the lower right square.

-17	-153x	-85
11x	99x²	55x
	9x	5

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 -153x and -85. The greatest common factor of -153x and -85 is -17. Therefore, we write -17 to the left of the top row. You can see it here in the color green:

-17	-153x	-85
11x	99x²	55x
	9x	5

Next, let’s look at the bottom row. We have the terms 99x² and 55x. The greatest common factor of 99x² and 55x is 11x. Therefore, we write 11x to the left of the bottom row. You can see it here in the color blue:

-17	-153x	-85
11x	99x²	55x
	9x	5

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:

-17	-153x	-85
11x	99x²	55x
	9x	5

Next, we divide 55x by 11x (labeled in blue). This gives us 5.

55x ÷ 11x = 5

You can see this value colored in purple below:

-17	-153x	-85
11x	99x²	55x
	9x	5

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 - 98x - 85. 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 - 17)(9x + 5)

That’s it! Now you know how to factor the equation 99x² - 98x - 85.

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