Factor 69x² + 97x + 28

Here we will show you how to factor the quadratic function 69x² + 97x + 28 using the box method. In other words, we will show you how to factor 69x squared plus 97x plus 28 (69x^2 + 97x + 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 69x² + 97x + 28, like this:

a = 69
b = 97
c = 28

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

28	28x	28
69x	69x²	69x
	x	1

We put 69x² (a) in the bottom left square and 28 (c) in the top right square, like this:

28	28x	28
69x	69x²	69x
	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 69 times 28 (a × c), and add together to equal 97 (b).

More specifically, 69 times 28 is 1932. Therefore, we need to find the two numbers that multiply to equal 1932, and add to equal 97.

? × ? = 1932
? + ? = 97

After looking at this problem, we can see that the two numbers that multiply together to equal 1932, and add together to equal 97, are 28 and 69, as illustrated here:

28 × 69 = 1932
28 + 69 = 97

Now, we can fill in the last two squares in our box with 28x and 69x. Place 28x in the upper left square, and place 69x in the lower right square.

28	28x	28
69x	69x²	69x
	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
69x	69x²	69x
	x	1

Next, let’s look at the bottom row. We have the terms 69x² and 69x. The greatest common factor of 69x² and 69x is 69x. Therefore, we write 69x to the left of the bottom row. You can see it here in the color blue:

28	28x	28
69x	69x²	69x
	x	1

To find the values below the table, we first divide 69x² by 69x (labeled in blue). This gives us x.

69x² ÷ 69x = x

You can see this value colored in orange below:

28	28x	28
69x	69x²	69x
	x	1

Next, we divide 69x by 69x (labeled in blue). This gives us 1.

69x ÷ 69x = 1

You can see this value colored in purple below:

28	28x	28
69x	69x²	69x
	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 69x² + 97x + 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:

(69x + 28)(x + 1)

That’s it! Now you know how to factor the equation 69x² + 97x + 28.

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

Factor 69x² + 97x + 34
Here is the next quadratic function on our list that we have factored for you.