Factor 92x² - 96x

Factor 92x² - 96x - 63

Here we will show you how to factor the quadratic function 92x² - 96x - 63 using the box method. In other words, we will show you how to factor 92x squared minus 96x minus 63 (92x^2 - 96x - 63) 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 92x² - 96x - 63, like this:

a = 92
b = -96
c = -63

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

-3	-138x	-63
2x	92x²	42x
	46x	21

We put 92x² (a) in the bottom left square and -63 (c) in the top right square, like this:

-3	-138x	-63
2x	92x²	42x
	46x	21

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 92 times -63 (a × c), and add together to equal -96 (b).

More specifically, 92 times -63 is -5796. Therefore, we need to find the two numbers that multiply to equal -5796, and add to equal -96.

? × ? = -5796
? + ? = -96

After looking at this problem, we can see that the two numbers that multiply together to equal -5796, and add together to equal -96, are -138 and 42, as illustrated here:

-138 × 42 = -5796
-138 + 42 = -96

Now, we can fill in the last two squares in our box with -138x and 42x. Place -138x in the upper left square, and place 42x in the lower right square.

-3	-138x	-63
2x	92x²	42x
	46x	21

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 -138x and -63. The greatest common factor of -138x and -63 is -3. Therefore, we write -3 to the left of the top row. You can see it here in the color green:

-3	-138x	-63
2x	92x²	42x
	46x	21

Next, let’s look at the bottom row. We have the terms 92x² and 42x. The greatest common factor of 92x² and 42x is 2x. Therefore, we write 2x to the left of the bottom row. You can see it here in the color blue:

-3	-138x	-63
2x	92x²	42x
	46x	21

To find the values below the table, we first divide 92x² by 2x (labeled in blue). This gives us 46x.

92x² ÷ 2x = 46x

You can see this value colored in orange below:

-3	-138x	-63
2x	92x²	42x
	46x	21

Next, we divide 42x by 2x (labeled in blue). This gives us 21.

42x ÷ 2x = 21

You can see this value colored in purple below:

-3	-138x	-63
2x	92x²	42x
	46x	21

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 92x² - 96x - 63. 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:

(2x - 3)(46x + 21)

That’s it! Now you know how to factor the equation 92x² - 96x - 63.

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