Factor 88x² - 30x

Factor 88x² - 30x - 100

Here we will show you how to factor the quadratic function 88x² - 30x - 100 using the box method. In other words, we will show you how to factor 88x squared minus 30x minus 100 (88x^2 - 30x - 100) 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 - 30x - 100, like this:

a = 88
b = -30
c = -100

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

-10	-110x	-100
8x	88x²	80x
	11x	10

We put 88x² (a) in the bottom left square and -100 (c) in the top right square, like this:

-10	-110x	-100
8x	88x²	80x
	11x	10

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 -100 (a × c), and add together to equal -30 (b).

More specifically, 88 times -100 is -8800. Therefore, we need to find the two numbers that multiply to equal -8800, and add to equal -30.

? × ? = -8800
? + ? = -30

After looking at this problem, we can see that the two numbers that multiply together to equal -8800, and add together to equal -30, are -110 and 80, as illustrated here:

-110 × 80 = -8800
-110 + 80 = -30

Now, we can fill in the last two squares in our box with -110x and 80x. Place -110x in the upper left square, and place 80x in the lower right square.

-10	-110x	-100
8x	88x²	80x
	11x	10

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 -110x and -100. The greatest common factor of -110x and -100 is -10. Therefore, we write -10 to the left of the top row. You can see it here in the color green:

-10	-110x	-100
8x	88x²	80x
	11x	10

Next, let’s look at the bottom row. We have the terms 88x² and 80x. The greatest common factor of 88x² and 80x is 8x. Therefore, we write 8x to the left of the bottom row. You can see it here in the color blue:

-10	-110x	-100
8x	88x²	80x
	11x	10

To find the values below the table, we first divide 88x² by 8x (labeled in blue). This gives us 11x.

88x² ÷ 8x = 11x

You can see this value colored in orange below:

-10	-110x	-100
8x	88x²	80x
	11x	10

Next, we divide 80x by 8x (labeled in blue). This gives us 10.

80x ÷ 8x = 10

You can see this value colored in purple below:

-10	-110x	-100
8x	88x²	80x
	11x	10

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 - 30x - 100. 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:

(8x - 10)(11x + 10)

That’s it! Now you know how to factor the equation 88x² - 30x - 100.

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