Factor 88x² - 98x

Factor 88x² - 98x - 30

Here we will show you how to factor the quadratic function 88x² - 98x - 30 using the box method. In other words, we will show you how to factor 88x squared minus 98x minus 30 (88x^2 - 98x - 30) 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 88x² - 98x - 30, like this:

a = 88
b = -98
c = -30

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

-30	-120x	-30
22x	88x²	22x
	4x	1

We put 88x² (a) in the bottom left square and -30 (c) in the top right square, like this:

-30	-120x	-30
22x	88x²	22x
	4x	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 88 times -30 (a × c), and add together to equal -98 (b).

More specifically, 88 times -30 is -2640. Therefore, we need to find the two numbers that multiply to equal -2640, and add to equal -98.

? × ? = -2640
? + ? = -98

After looking at this problem, we can see that the two numbers that multiply together to equal -2640, and add together to equal -98, are -120 and 22, as illustrated here:

-120 × 22 = -2640
-120 + 22 = -98

Now, we can fill in the last two squares in our box with -120x and 22x. Place -120x in the upper left square, and place 22x in the lower right square.

-30	-120x	-30
22x	88x²	22x
	4x	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 -120x and -30. The greatest common factor of -120x and -30 is -30. Therefore, we write -30 to the left of the top row. You can see it here in the color green:

-30	-120x	-30
22x	88x²	22x
	4x	1

Next, let’s look at the bottom row. We have the terms 88x² and 22x. The greatest common factor of 88x² and 22x is 22x. Therefore, we write 22x to the left of the bottom row. You can see it here in the color blue:

-30	-120x	-30
22x	88x²	22x
	4x	1

To find the values below the table, we first divide 88x² by 22x (labeled in blue). This gives us 4x.

88x² ÷ 22x = 4x

You can see this value colored in orange below:

-30	-120x	-30
22x	88x²	22x
	4x	1

Next, we divide 22x by 22x (labeled in blue). This gives us 1.

22x ÷ 22x = 1

You can see this value colored in purple below:

-30	-120x	-30
22x	88x²	22x
	4x	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 88x² - 98x - 30. 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:

(22x - 30)(4x + 1)

That’s it! Now you know how to factor the equation 88x² - 98x - 30.

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