Factor 94x² + 75x + 14

Here we will show you how to factor the quadratic function 94x² + 75x + 14 using the box method. In other words, we will show you how to factor 94x squared plus 75x plus 14 (94x^2 + 75x + 14) 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 94x² + 75x + 14, like this:

a = 94
b = 75
c = 14

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

14	28x	14
47x	94x²	47x
	2x	1

We put 94x² (a) in the bottom left square and 14 (c) in the top right square, like this:

14	28x	14
47x	94x²	47x
	2x	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 94 times 14 (a × c), and add together to equal 75 (b).

More specifically, 94 times 14 is 1316. Therefore, we need to find the two numbers that multiply to equal 1316, and add to equal 75.

? × ? = 1316
? + ? = 75

After looking at this problem, we can see that the two numbers that multiply together to equal 1316, and add together to equal 75, are 28 and 47, as illustrated here:

28 × 47 = 1316
28 + 47 = 75

Now, we can fill in the last two squares in our box with 28x and 47x. Place 28x in the upper left square, and place 47x in the lower right square.

14	28x	14
47x	94x²	47x
	2x	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 14. The greatest common factor of 28x and 14 is 14. Therefore, we write 14 to the left of the top row. You can see it here in the color green:

14	28x	14
47x	94x²	47x
	2x	1

Next, let’s look at the bottom row. We have the terms 94x² and 47x. The greatest common factor of 94x² and 47x is 47x. Therefore, we write 47x to the left of the bottom row. You can see it here in the color blue:

14	28x	14
47x	94x²	47x
	2x	1

To find the values below the table, we first divide 94x² by 47x (labeled in blue). This gives us 2x.

94x² ÷ 47x = 2x

You can see this value colored in orange below:

14	28x	14
47x	94x²	47x
	2x	1

Next, we divide 47x by 47x (labeled in blue). This gives us 1.

47x ÷ 47x = 1

You can see this value colored in purple below:

14	28x	14
47x	94x²	47x
	2x	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 94x² + 75x + 14. 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:

(47x + 14)(2x + 1)

That’s it! Now you know how to factor the equation 94x² + 75x + 14.

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

Factor 94x² + 76x - 18
Here is the next quadratic function on our list that we have factored for you.