Factor 44x² + 53x + 9

Here we will show you how to factor the quadratic function 44x² + 53x + 9 using the box method. In other words, we will show you how to factor 44x squared plus 53x plus 9 (44x^2 + 53x + 9) 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 44x² + 53x + 9, like this:

a = 44
b = 53
c = 9

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

9	9x	9
44x	44x²	44x
	x	1

We put 44x² (a) in the bottom left square and 9 (c) in the top right square, like this:

9	9x	9
44x	44x²	44x
	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 44 times 9 (a × c), and add together to equal 53 (b).

More specifically, 44 times 9 is 396. Therefore, we need to find the two numbers that multiply to equal 396, and add to equal 53.

? × ? = 396
? + ? = 53

After looking at this problem, we can see that the two numbers that multiply together to equal 396, and add together to equal 53, are 9 and 44, as illustrated here:

9 × 44 = 396
9 + 44 = 53

Now, we can fill in the last two squares in our box with 9x and 44x. Place 9x in the upper left square, and place 44x in the lower right square.

9	9x	9
44x	44x²	44x
	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 9x and 9. The greatest common factor of 9x and 9 is 9. Therefore, we write 9 to the left of the top row. You can see it here in the color green:

9	9x	9
44x	44x²	44x
	x	1

Next, let’s look at the bottom row. We have the terms 44x² and 44x. The greatest common factor of 44x² and 44x is 44x. Therefore, we write 44x to the left of the bottom row. You can see it here in the color blue:

9	9x	9
44x	44x²	44x
	x	1

To find the values below the table, we first divide 44x² by 44x (labeled in blue). This gives us x.

44x² ÷ 44x = x

You can see this value colored in orange below:

9	9x	9
44x	44x²	44x
	x	1

Next, we divide 44x by 44x (labeled in blue). This gives us 1.

44x ÷ 44x = 1

You can see this value colored in purple below:

9	9x	9
44x	44x²	44x
	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 44x² + 53x + 9. 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:

(44x + 9)(x + 1)

That’s it! Now you know how to factor the equation 44x² + 53x + 9.

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