Factor 32x² + 60x + 28

Here we will show you how to factor the quadratic function 32x² + 60x + 28 using the box method. In other words, we will show you how to factor 32x squared plus 60x plus 28 (32x^2 + 60x + 28) 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 32x² + 60x + 28, like this:

a = 32
b = 60
c = 28

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

28	28x	28
32x	32x²	32x
	x	1

We put 32x² (a) in the bottom left square and 28 (c) in the top right square, like this:

28	28x	28
32x	32x²	32x
	x	1

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 32 times 28 (a × c), and add together to equal 60 (b).

More specifically, 32 times 28 is 896. Therefore, we need to find the two numbers that multiply to equal 896, and add to equal 60.

? × ? = 896
? + ? = 60

After looking at this problem, we can see that the two numbers that multiply together to equal 896, and add together to equal 60, are 28 and 32, as illustrated here:

28 × 32 = 896
28 + 32 = 60

Now, we can fill in the last two squares in our box with 28x and 32x. Place 28x in the upper left square, and place 32x in the lower right square.

28	28x	28
32x	32x²	32x
	x	1

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

28	28x	28
32x	32x²	32x
	x	1

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

28	28x	28
32x	32x²	32x
	x	1

To find the values below the table, we first divide 32x² by 32x (labeled in blue). This gives us x.

32x² ÷ 32x = x

You can see this value colored in orange below:

28	28x	28
32x	32x²	32x
	x	1

Next, we divide 32x by 32x (labeled in blue). This gives us 1.

32x ÷ 32x = 1

You can see this value colored in purple below:

28	28x	28
32x	32x²	32x
	x	1

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 32x² + 60x + 28. 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:

(32x + 28)(x + 1)

That’s it! Now you know how to factor the equation 32x² + 60x + 28.

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

Factor 32x² + 61x - 93
Here is the next quadratic function on our list that we have factored for you.