Factor 11x² - 95x + 84

Here we will show you how to factor the quadratic function 11x² - 95x + 84 using the box method. In other words, we will show you how to factor 11x squared minus 95x plus 84 (11x^2 - 95x + 84) 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 11x² - 95x + 84, like this:

a = 11
b = -95
c = 84

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

-84	-84x	84
11x	11x²	-11x
	x	-1

We put 11x² (a) in the bottom left square and 84 (c) in the top right square, like this:

-84	-84x	84
11x	11x²	-11x
	x	-1

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 11 times 84 (a × c), and add together to equal -95 (b).

More specifically, 11 times 84 is 924. Therefore, we need to find the two numbers that multiply to equal 924, and add to equal -95.

? × ? = 924
? + ? = -95

After looking at this problem, we can see that the two numbers that multiply together to equal 924, and add together to equal -95, are -84 and -11, as illustrated here:

-84 × -11 = 924
-84 + -11 = -95

Now, we can fill in the last two squares in our box with -84x and -11x. Place -84x in the upper left square, and place -11x in the lower right square.

-84	-84x	84
11x	11x²	-11x
	x	-1

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 -84x and 84. The greatest common factor of -84x and 84 is -84. Therefore, we write -84 to the left of the top row. You can see it here in the color green:

-84	-84x	84
11x	11x²	-11x
	x	-1

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

-84	-84x	84
11x	11x²	-11x
	x	-1

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

11x² ÷ 11x = x

You can see this value colored in orange below:

-84	-84x	84
11x	11x²	-11x
	x	-1

Next, we divide -11x by 11x (labeled in blue). This gives us -1.

-11x ÷ 11x = -1

You can see this value colored in purple below:

-84	-84x	84
11x	11x²	-11x
	x	-1

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 11x² - 95x + 84. 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 - 84)(x - 1)

That’s it! Now you know how to factor the equation 11x² - 95x + 84.

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