Factor 26x² - 100x + 96

Here we will show you how to factor the quadratic function 26x² - 100x + 96 using the box method. In other words, we will show you how to factor 26x squared minus 100x plus 96 (26x^2 - 100x + 96) 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 26x² - 100x + 96, like this:

a = 26
b = -100
c = 96

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

-4	-52x	96
2x	26x²	-48x
	13x	-24

We put 26x² (a) in the bottom left square and 96 (c) in the top right square, like this:

-4	-52x	96
2x	26x²	-48x
	13x	-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 26 times 96 (a × c), and add together to equal -100 (b).

More specifically, 26 times 96 is 2496. Therefore, we need to find the two numbers that multiply to equal 2496, and add to equal -100.

? × ? = 2496
? + ? = -100

After looking at this problem, we can see that the two numbers that multiply together to equal 2496, and add together to equal -100, are -52 and -48, as illustrated here:

-52 × -48 = 2496
-52 + -48 = -100

Now, we can fill in the last two squares in our box with -52x and -48x. Place -52x in the upper left square, and place -48x in the lower right square.

-4	-52x	96
2x	26x²	-48x
	13x	-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 -52x and 96. The greatest common factor of -52x and 96 is -4. Therefore, we write -4 to the left of the top row. You can see it here in the color green:

-4	-52x	96
2x	26x²	-48x
	13x	-24

Next, let’s look at the bottom row. We have the terms 26x² and -48x. The greatest common factor of 26x² and -48x is 2x. Therefore, we write 2x to the left of the bottom row. You can see it here in the color blue:

-4	-52x	96
2x	26x²	-48x
	13x	-24

To find the values below the table, we first divide 26x² by 2x (labeled in blue). This gives us 13x.

26x² ÷ 2x = 13x

You can see this value colored in orange below:

-4	-52x	96
2x	26x²	-48x
	13x	-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:

-4	-52x	96
2x	26x²	-48x
	13x	-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 26x² - 100x + 96. 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 - 4)(13x - 24)

That’s it! Now you know how to factor the equation 26x² - 100x + 96.

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