Factor 98x² - 99x

Factor 98x² - 99x - 72

Here we will show you how to factor the quadratic function 98x² - 99x - 72 using the box method. In other words, we will show you how to factor 98x squared minus 99x minus 72 (98x^2 - 99x - 72) 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 98x² - 99x - 72, like this:

a = 98
b = -99
c = -72

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

-3	-147x	-72
2x	98x²	48x
	49x	24

We put 98x² (a) in the bottom left square and -72 (c) in the top right square, like this:

-3	-147x	-72
2x	98x²	48x
	49x	24

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 98 times -72 (a × c), and add together to equal -99 (b).

More specifically, 98 times -72 is -7056. Therefore, we need to find the two numbers that multiply to equal -7056, and add to equal -99.

? × ? = -7056
? + ? = -99

After looking at this problem, we can see that the two numbers that multiply together to equal -7056, and add together to equal -99, are -147 and 48, as illustrated here:

-147 × 48 = -7056
-147 + 48 = -99

Now, we can fill in the last two squares in our box with -147x and 48x. Place -147x in the upper left square, and place 48x in the lower right square.

-3	-147x	-72
2x	98x²	48x
	49x	24

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 -147x and -72. The greatest common factor of -147x and -72 is -3. Therefore, we write -3 to the left of the top row. You can see it here in the color green:

-3	-147x	-72
2x	98x²	48x
	49x	24

Next, let’s look at the bottom row. We have the terms 98x² and 48x. The greatest common factor of 98x² and 48x is 2x. Therefore, we write 2x to the left of the bottom row. You can see it here in the color blue:

-3	-147x	-72
2x	98x²	48x
	49x	24

To find the values below the table, we first divide 98x² by 2x (labeled in blue). This gives us 49x.

98x² ÷ 2x = 49x

You can see this value colored in orange below:

-3	-147x	-72
2x	98x²	48x
	49x	24

Next, we divide 48x by 2x (labeled in blue). This gives us 24.

48x ÷ 2x = 24

You can see this value colored in purple below:

-3	-147x	-72
2x	98x²	48x
	49x	24

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 98x² - 99x - 72. 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)(49x + 24)

That’s it! Now you know how to factor the equation 98x² - 99x - 72.

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