Factor 93x² - 88x

Factor 93x² - 88x - 48

Here we will show you how to factor the quadratic function 93x² - 88x - 48 using the box method. In other words, we will show you how to factor 93x squared minus 88x minus 48 (93x^2 - 88x - 48) 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 93x² - 88x - 48, like this:

a = 93
b = -88
c = -48

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

-4	-124x	-48
3x	93x²	36x
	31x	12

We put 93x² (a) in the bottom left square and -48 (c) in the top right square, like this:

-4	-124x	-48
3x	93x²	36x
	31x	12

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 93 times -48 (a × c), and add together to equal -88 (b).

More specifically, 93 times -48 is -4464. Therefore, we need to find the two numbers that multiply to equal -4464, and add to equal -88.

? × ? = -4464
? + ? = -88

After looking at this problem, we can see that the two numbers that multiply together to equal -4464, and add together to equal -88, are -124 and 36, as illustrated here:

-124 × 36 = -4464
-124 + 36 = -88

Now, we can fill in the last two squares in our box with -124x and 36x. Place -124x in the upper left square, and place 36x in the lower right square.

-4	-124x	-48
3x	93x²	36x
	31x	12

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 -124x and -48. The greatest common factor of -124x and -48 is -4. Therefore, we write -4 to the left of the top row. You can see it here in the color green:

-4	-124x	-48
3x	93x²	36x
	31x	12

Next, let’s look at the bottom row. We have the terms 93x² and 36x. The greatest common factor of 93x² and 36x is 3x. Therefore, we write 3x to the left of the bottom row. You can see it here in the color blue:

-4	-124x	-48
3x	93x²	36x
	31x	12

To find the values below the table, we first divide 93x² by 3x (labeled in blue). This gives us 31x.

93x² ÷ 3x = 31x

You can see this value colored in orange below:

-4	-124x	-48
3x	93x²	36x
	31x	12

Next, we divide 36x by 3x (labeled in blue). This gives us 12.

36x ÷ 3x = 12

You can see this value colored in purple below:

-4	-124x	-48
3x	93x²	36x
	31x	12

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 93x² - 88x - 48. 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:

(3x - 4)(31x + 12)

That’s it! Now you know how to factor the equation 93x² - 88x - 48.

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