Factor 60x² + 62x + 14

Here we will show you how to factor the quadratic function 60x² + 62x + 14 using the box method. In other words, we will show you how to factor 60x squared plus 62x plus 14 (60x^2 + 62x + 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 60x² + 62x + 14, like this:

a = 60
b = 62
c = 14

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

2	20x	14
6x	60x²	42x
	10x	7

We put 60x² (a) in the bottom left square and 14 (c) in the top right square, like this:

2	20x	14
6x	60x²	42x
	10x	7

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 60 times 14 (a × c), and add together to equal 62 (b).

More specifically, 60 times 14 is 840. Therefore, we need to find the two numbers that multiply to equal 840, and add to equal 62.

? × ? = 840
? + ? = 62

After looking at this problem, we can see that the two numbers that multiply together to equal 840, and add together to equal 62, are 20 and 42, as illustrated here:

20 × 42 = 840
20 + 42 = 62

Now, we can fill in the last two squares in our box with 20x and 42x. Place 20x in the upper left square, and place 42x in the lower right square.

2	20x	14
6x	60x²	42x
	10x	7

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 14. The greatest common factor of 20x and 14 is 2. Therefore, we write 2 to the left of the top row. You can see it here in the color green:

2	20x	14
6x	60x²	42x
	10x	7

Next, let’s look at the bottom row. We have the terms 60x² and 42x. The greatest common factor of 60x² and 42x is 6x. Therefore, we write 6x to the left of the bottom row. You can see it here in the color blue:

2	20x	14
6x	60x²	42x
	10x	7

To find the values below the table, we first divide 60x² by 6x (labeled in blue). This gives us 10x.

60x² ÷ 6x = 10x

You can see this value colored in orange below:

2	20x	14
6x	60x²	42x
	10x	7

Next, we divide 42x by 6x (labeled in blue). This gives us 7.

42x ÷ 6x = 7

You can see this value colored in purple below:

2	20x	14
6x	60x²	42x
	10x	7

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 60x² + 62x + 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:

(6x + 2)(10x + 7)

That’s it! Now you know how to factor the equation 60x² + 62x + 14.

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

Factor 60x² + 62x + 16
Here is the next quadratic function on our list that we have factored for you.