Factor 20x² + 68x + 56

Here we will show you how to factor the quadratic function 20x² + 68x + 56 using the box method. In other words, we will show you how to factor 20x squared plus 68x plus 56 (20x^2 + 68x + 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 20x² + 68x + 56, like this:

a = 20
b = 68
c = 56

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

28	28x	56
20x	20x²	40x
	x	2

We put 20x² (a) in the bottom left square and 56 (c) in the top right square, like this:

28	28x	56
20x	20x²	40x
	x	2

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 20 times 56 (a × c), and add together to equal 68 (b).

More specifically, 20 times 56 is 1120. Therefore, we need to find the two numbers that multiply to equal 1120, and add to equal 68.

? × ? = 1120
? + ? = 68

After looking at this problem, we can see that the two numbers that multiply together to equal 1120, and add together to equal 68, are 28 and 40, as illustrated here:

28 × 40 = 1120
28 + 40 = 68

Now, we can fill in the last two squares in our box with 28x and 40x. Place 28x in the upper left square, and place 40x in the lower right square.

28	28x	56
20x	20x²	40x
	x	2

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 28x and 56. The greatest common factor of 28x and 56 is 28. Therefore, we write 28 to the left of the top row. You can see it here in the color green:

28	28x	56
20x	20x²	40x
	x	2

Next, let’s look at the bottom row. We have the terms 20x² and 40x. The greatest common factor of 20x² and 40x is 20x. Therefore, we write 20x to the left of the bottom row. You can see it here in the color blue:

28	28x	56
20x	20x²	40x
	x	2

To find the values below the table, we first divide 20x² by 20x (labeled in blue). This gives us x.

20x² ÷ 20x = x

You can see this value colored in orange below:

28	28x	56
20x	20x²	40x
	x	2

Next, we divide 40x by 20x (labeled in blue). This gives us 2.

40x ÷ 20x = 2

You can see this value colored in purple below:

28	28x	56
20x	20x²	40x
	x	2

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 20x² + 68x + 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:

(20x + 28)(x + 2)

That’s it! Now you know how to factor the equation 20x² + 68x + 56.

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Factor 20x² + 68x + 57
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