Factor 47x² - 51x

Factor 47x² - 51x - 98

Here we will show you how to factor the quadratic function 47x² - 51x - 98 using the box method. In other words, we will show you how to factor 47x squared minus 51x minus 98 (47x^2 - 51x - 98) 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 47x² - 51x - 98, like this:

a = 47
b = -51
c = -98

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

-98	-98x	-98
47x	47x²	47x
	x	1

We put 47x² (a) in the bottom left square and -98 (c) in the top right square, like this:

-98	-98x	-98
47x	47x²	47x
	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 47 times -98 (a × c), and add together to equal -51 (b).

More specifically, 47 times -98 is -4606. Therefore, we need to find the two numbers that multiply to equal -4606, and add to equal -51.

? × ? = -4606
? + ? = -51

After looking at this problem, we can see that the two numbers that multiply together to equal -4606, and add together to equal -51, are -98 and 47, as illustrated here:

-98 × 47 = -4606
-98 + 47 = -51

Now, we can fill in the last two squares in our box with -98x and 47x. Place -98x in the upper left square, and place 47x in the lower right square.

-98	-98x	-98
47x	47x²	47x
	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 -98x and -98. The greatest common factor of -98x and -98 is -98. Therefore, we write -98 to the left of the top row. You can see it here in the color green:

-98	-98x	-98
47x	47x²	47x
	x	1

Next, let’s look at the bottom row. We have the terms 47x² and 47x. The greatest common factor of 47x² and 47x is 47x. Therefore, we write 47x to the left of the bottom row. You can see it here in the color blue:

-98	-98x	-98
47x	47x²	47x
	x	1

To find the values below the table, we first divide 47x² by 47x (labeled in blue). This gives us x.

47x² ÷ 47x = x

You can see this value colored in orange below:

-98	-98x	-98
47x	47x²	47x
	x	1

Next, we divide 47x by 47x (labeled in blue). This gives us 1.

47x ÷ 47x = 1

You can see this value colored in purple below:

-98	-98x	-98
47x	47x²	47x
	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 47x² - 51x - 98. 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:

(47x - 98)(x + 1)

That’s it! Now you know how to factor the equation 47x² - 51x - 98.

Factoring Quadratics
Go here if you want to learn how to factor another quadratic function.

Factor 47x² - 51x - 86
Here is the next quadratic function on our list that we have factored for you.