Factor 99x² - 93x + 18

Here we will show you how to factor the quadratic function 99x² - 93x + 18 using the box method. In other words, we will show you how to factor 99x squared minus 93x plus 18 (99x^2 - 93x + 18) 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 - 93x + 18, like this:

a = 99
b = -93
c = 18

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

-6	-66x	18
9x	99x²	-27x
	11x	-3

We put 99x² (a) in the bottom left square and 18 (c) in the top right square, like this:

-6	-66x	18
9x	99x²	-27x
	11x	-3

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 18 (a × c), and add together to equal -93 (b).

More specifically, 99 times 18 is 1782. Therefore, we need to find the two numbers that multiply to equal 1782, and add to equal -93.

? × ? = 1782
? + ? = -93

After looking at this problem, we can see that the two numbers that multiply together to equal 1782, and add together to equal -93, are -66 and -27, as illustrated here:

-66 × -27 = 1782
-66 + -27 = -93

Now, we can fill in the last two squares in our box with -66x and -27x. Place -66x in the upper left square, and place -27x in the lower right square.

-6	-66x	18
9x	99x²	-27x
	11x	-3

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 -66x and 18. The greatest common factor of -66x and 18 is -6. Therefore, we write -6 to the left of the top row. You can see it here in the color green:

-6	-66x	18
9x	99x²	-27x
	11x	-3

Next, let’s look at the bottom row. We have the terms 99x² and -27x. The greatest common factor of 99x² and -27x is 9x. Therefore, we write 9x to the left of the bottom row. You can see it here in the color blue:

-6	-66x	18
9x	99x²	-27x
	11x	-3

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

99x² ÷ 9x = 11x

You can see this value colored in orange below:

-6	-66x	18
9x	99x²	-27x
	11x	-3

Next, we divide -27x by 9x (labeled in blue). This gives us -3.

-27x ÷ 9x = -3

You can see this value colored in purple below:

-6	-66x	18
9x	99x²	-27x
	11x	-3

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 - 93x + 18. 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:

(9x - 6)(11x - 3)

That’s it! Now you know how to factor the equation 99x² - 93x + 18.

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