Factor 28x² + 38x + 12

Here we will show you how to factor the quadratic function 28x² + 38x + 12 using the box method. In other words, we will show you how to factor 28x squared plus 38x plus 12 (28x^2 + 38x + 12) 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 28x² + 38x + 12, like this:

a = 28
b = 38
c = 12

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

2	14x	12
4x	28x²	24x
	7x	6

We put 28x² (a) in the bottom left square and 12 (c) in the top right square, like this:

2	14x	12
4x	28x²	24x
	7x	6

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 28 times 12 (a × c), and add together to equal 38 (b).

More specifically, 28 times 12 is 336. Therefore, we need to find the two numbers that multiply to equal 336, and add to equal 38.

? × ? = 336
? + ? = 38

After looking at this problem, we can see that the two numbers that multiply together to equal 336, and add together to equal 38, are 14 and 24, as illustrated here:

14 × 24 = 336
14 + 24 = 38

Now, we can fill in the last two squares in our box with 14x and 24x. Place 14x in the upper left square, and place 24x in the lower right square.

2	14x	12
4x	28x²	24x
	7x	6

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 14x and 12. The greatest common factor of 14x and 12 is 2. Therefore, we write 2 to the left of the top row. You can see it here in the color green:

2	14x	12
4x	28x²	24x
	7x	6

Next, let’s look at the bottom row. We have the terms 28x² and 24x. The greatest common factor of 28x² and 24x is 4x. Therefore, we write 4x to the left of the bottom row. You can see it here in the color blue:

2	14x	12
4x	28x²	24x
	7x	6

To find the values below the table, we first divide 28x² by 4x (labeled in blue). This gives us 7x.

28x² ÷ 4x = 7x

You can see this value colored in orange below:

2	14x	12
4x	28x²	24x
	7x	6

Next, we divide 24x by 4x (labeled in blue). This gives us 6.

24x ÷ 4x = 6

You can see this value colored in purple below:

2	14x	12
4x	28x²	24x
	7x	6

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 28x² + 38x + 12. 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:

(4x + 2)(7x + 6)

That’s it! Now you know how to factor the equation 28x² + 38x + 12.

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