Factor 88x² - 98x + 24

Here we will show you how to factor the quadratic function 88x² - 98x + 24 using the box method. In other words, we will show you how to factor 88x squared minus 98x plus 24 (88x^2 - 98x + 24) 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 + 24, like this:

a = 88
b = -98
c = 24

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

-6	-66x	24
8x	88x²	-32x
	11x	-4

We put 88x² (a) in the bottom left square and 24 (c) in the top right square, like this:

-6	-66x	24
8x	88x²	-32x
	11x	-4

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 24 (a × c), and add together to equal -98 (b).

More specifically, 88 times 24 is 2112. Therefore, we need to find the two numbers that multiply to equal 2112, and add to equal -98.

? × ? = 2112
? + ? = -98

After looking at this problem, we can see that the two numbers that multiply together to equal 2112, and add together to equal -98, are -66 and -32, as illustrated here:

-66 × -32 = 2112
-66 + -32 = -98

Now, we can fill in the last two squares in our box with -66x and -32x. Place -66x in the upper left square, and place -32x in the lower right square.

-6	-66x	24
8x	88x²	-32x
	11x	-4

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 -66x and 24. The greatest common factor of -66x and 24 is -6. Therefore, we write -6 to the left of the top row. You can see it here in the color green:

-6	-66x	24
8x	88x²	-32x
	11x	-4

Next, let’s look at the bottom row. We have the terms 88x² and -32x. The greatest common factor of 88x² and -32x is 8x. Therefore, we write 8x to the left of the bottom row. You can see it here in the color blue:

-6	-66x	24
8x	88x²	-32x
	11x	-4

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:

-6	-66x	24
8x	88x²	-32x
	11x	-4

Next, we divide -32x by 8x (labeled in blue). This gives us -4.

-32x ÷ 8x = -4

You can see this value colored in purple below:

-6	-66x	24
8x	88x²	-32x
	11x	-4

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 + 24. 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 - 6)(11x - 4)

That’s it! Now you know how to factor the equation 88x² - 98x + 24.

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