Factor 56x² - 15x

Factor 56x² - 15x - 56

Here we will show you how to factor the quadratic function 56x² - 15x - 56 using the box method. In other words, we will show you how to factor 56x squared minus 15x minus 56 (56x^2 - 15x - 56) 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 56x² - 15x - 56, like this:

a = 56
b = -15
c = -56

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

-8	-64x	-56
7x	56x²	49x
	8x	7

We put 56x² (a) in the bottom left square and -56 (c) in the top right square, like this:

-8	-64x	-56
7x	56x²	49x
	8x	7

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 56 times -56 (a × c), and add together to equal -15 (b).

More specifically, 56 times -56 is -3136. Therefore, we need to find the two numbers that multiply to equal -3136, and add to equal -15.

? × ? = -3136
? + ? = -15

After looking at this problem, we can see that the two numbers that multiply together to equal -3136, and add together to equal -15, are -64 and 49, as illustrated here:

-64 × 49 = -3136
-64 + 49 = -15

Now, we can fill in the last two squares in our box with -64x and 49x. Place -64x in the upper left square, and place 49x in the lower right square.

-8	-64x	-56
7x	56x²	49x
	8x	7

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 -64x and -56. The greatest common factor of -64x and -56 is -8. Therefore, we write -8 to the left of the top row. You can see it here in the color green:

-8	-64x	-56
7x	56x²	49x
	8x	7

Next, let’s look at the bottom row. We have the terms 56x² and 49x. The greatest common factor of 56x² and 49x is 7x. Therefore, we write 7x to the left of the bottom row. You can see it here in the color blue:

-8	-64x	-56
7x	56x²	49x
	8x	7

To find the values below the table, we first divide 56x² by 7x (labeled in blue). This gives us 8x.

56x² ÷ 7x = 8x

You can see this value colored in orange below:

-8	-64x	-56
7x	56x²	49x
	8x	7

Next, we divide 49x by 7x (labeled in blue). This gives us 7.

49x ÷ 7x = 7

You can see this value colored in purple below:

-8	-64x	-56
7x	56x²	49x
	8x	7

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 56x² - 15x - 56. 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:

(7x - 8)(8x + 7)

That’s it! Now you know how to factor the equation 56x² - 15x - 56.

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