Factor 25x² + 90x + 56

Here we will show you how to factor the quadratic function 25x² + 90x + 56 using the box method. In other words, we will show you how to factor 25x squared plus 90x plus 56 (25x^2 + 90x + 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 25x² + 90x + 56, like this:

a = 25
b = 90
c = 56

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

4	20x	56
5x	25x²	70x
	5x	14

We put 25x² (a) in the bottom left square and 56 (c) in the top right square, like this:

4	20x	56
5x	25x²	70x
	5x	14

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 25 times 56 (a × c), and add together to equal 90 (b).

More specifically, 25 times 56 is 1400. Therefore, we need to find the two numbers that multiply to equal 1400, and add to equal 90.

? × ? = 1400
? + ? = 90

After looking at this problem, we can see that the two numbers that multiply together to equal 1400, and add together to equal 90, are 20 and 70, as illustrated here:

20 × 70 = 1400
20 + 70 = 90

Now, we can fill in the last two squares in our box with 20x and 70x. Place 20x in the upper left square, and place 70x in the lower right square.

4	20x	56
5x	25x²	70x
	5x	14

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 20x and 56. The greatest common factor of 20x and 56 is 4. Therefore, we write 4 to the left of the top row. You can see it here in the color green:

4	20x	56
5x	25x²	70x
	5x	14

Next, let’s look at the bottom row. We have the terms 25x² and 70x. The greatest common factor of 25x² and 70x is 5x. Therefore, we write 5x to the left of the bottom row. You can see it here in the color blue:

4	20x	56
5x	25x²	70x
	5x	14

To find the values below the table, we first divide 25x² by 5x (labeled in blue). This gives us 5x.

25x² ÷ 5x = 5x

You can see this value colored in orange below:

4	20x	56
5x	25x²	70x
	5x	14

Next, we divide 70x by 5x (labeled in blue). This gives us 14.

70x ÷ 5x = 14

You can see this value colored in purple below:

4	20x	56
5x	25x²	70x
	5x	14

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 25x² + 90x + 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:

(5x + 4)(5x + 14)

That’s it! Now you know how to factor the equation 25x² + 90x + 56.

Factoring Quadratics
Go here if you want to learn how to factor another quadratic function.

Factor 25x² + 90x + 65
Here is the next quadratic function on our list that we have factored for you.