Factor 44x² + 59x + 12

Here we will show you how to factor the quadratic function 44x² + 59x + 12 using the box method. In other words, we will show you how to factor 44x squared plus 59x plus 12 (44x^2 + 59x + 12) 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 + 59x + 12, like this:

a = 44
b = 59
c = 12

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

1	11x	12
4x	44x²	48x
	11x	12

We put 44x² (a) in the bottom left square and 12 (c) in the top right square, like this:

1	11x	12
4x	44x²	48x
	11x	12

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 12 (a × c), and add together to equal 59 (b).

More specifically, 44 times 12 is 528. Therefore, we need to find the two numbers that multiply to equal 528, and add to equal 59.

? × ? = 528
? + ? = 59

After looking at this problem, we can see that the two numbers that multiply together to equal 528, and add together to equal 59, are 11 and 48, as illustrated here:

11 × 48 = 528
11 + 48 = 59

Now, we can fill in the last two squares in our box with 11x and 48x. Place 11x in the upper left square, and place 48x in the lower right square.

1	11x	12
4x	44x²	48x
	11x	12

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 11x and 12. The greatest common factor of 11x and 12 is 1. Therefore, we write 1 to the left of the top row. You can see it here in the color green:

1	11x	12
4x	44x²	48x
	11x	12

Next, let’s look at the bottom row. We have the terms 44x² and 48x. The greatest common factor of 44x² and 48x is 4x. Therefore, we write 4x to the left of the bottom row. You can see it here in the color blue:

1	11x	12
4x	44x²	48x
	11x	12

To find the values below the table, we first divide 44x² by 4x (labeled in blue). This gives us 11x.

44x² ÷ 4x = 11x

You can see this value colored in orange below:

1	11x	12
4x	44x²	48x
	11x	12

Next, we divide 48x by 4x (labeled in blue). This gives us 12.

48x ÷ 4x = 12

You can see this value colored in purple below:

1	11x	12
4x	44x²	48x
	11x	12

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 + 59x + 12. 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:

(4x + 1)(11x + 12)

That’s it! Now you know how to factor the equation 44x² + 59x + 12.

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