Factor 18x² + 49x + 33

Here we will show you how to factor the quadratic function 18x² + 49x + 33 using the box method. In other words, we will show you how to factor 18x squared plus 49x plus 33 (18x^2 + 49x + 33) 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 18x² + 49x + 33, like this:

a = 18
b = 49
c = 33

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

11	22x	33
9x	18x²	27x
	2x	3

We put 18x² (a) in the bottom left square and 33 (c) in the top right square, like this:

11	22x	33
9x	18x²	27x
	2x	3

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 18 times 33 (a × c), and add together to equal 49 (b).

More specifically, 18 times 33 is 594. Therefore, we need to find the two numbers that multiply to equal 594, and add to equal 49.

? × ? = 594
? + ? = 49

After looking at this problem, we can see that the two numbers that multiply together to equal 594, and add together to equal 49, are 22 and 27, as illustrated here:

22 × 27 = 594
22 + 27 = 49

Now, we can fill in the last two squares in our box with 22x and 27x. Place 22x in the upper left square, and place 27x in the lower right square.

11	22x	33
9x	18x²	27x
	2x	3

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 22x and 33. The greatest common factor of 22x and 33 is 11. Therefore, we write 11 to the left of the top row. You can see it here in the color green:

11	22x	33
9x	18x²	27x
	2x	3

Next, let’s look at the bottom row. We have the terms 18x² and 27x. The greatest common factor of 18x² and 27x is 9x. Therefore, we write 9x to the left of the bottom row. You can see it here in the color blue:

11	22x	33
9x	18x²	27x
	2x	3

To find the values below the table, we first divide 18x² by 9x (labeled in blue). This gives us 2x.

18x² ÷ 9x = 2x

You can see this value colored in orange below:

11	22x	33
9x	18x²	27x
	2x	3

Next, we divide 27x by 9x (labeled in blue). This gives us 3.

27x ÷ 9x = 3

You can see this value colored in purple below:

11	22x	33
9x	18x²	27x
	2x	3

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 18x² + 49x + 33. 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:

(9x + 11)(2x + 3)

That’s it! Now you know how to factor the equation 18x² + 49x + 33.

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

Factor 18x² + 50x - 88
Here is the next quadratic function on our list that we have factored for you.