Factor 44x² + 85x

Factor 44x² + 85x - 99

Here we will show you how to factor the quadratic function 44x² + 85x - 99 using the box method. In other words, we will show you how to factor 44x squared plus 85x minus 99 (44x^2 + 85x - 99) 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 + 85x - 99, like this:

a = 44
b = 85
c = -99

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

-9	-36x	-99
11x	44x²	121x
	4x	11

We put 44x² (a) in the bottom left square and -99 (c) in the top right square, like this:

-9	-36x	-99
11x	44x²	121x
	4x	11

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 -99 (a × c), and add together to equal 85 (b).

More specifically, 44 times -99 is -4356. Therefore, we need to find the two numbers that multiply to equal -4356, and add to equal 85.

? × ? = -4356
? + ? = 85

After looking at this problem, we can see that the two numbers that multiply together to equal -4356, and add together to equal 85, are -36 and 121, as illustrated here:

-36 × 121 = -4356
-36 + 121 = 85

Now, we can fill in the last two squares in our box with -36x and 121x. Place -36x in the upper left square, and place 121x in the lower right square.

-9	-36x	-99
11x	44x²	121x
	4x	11

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 -36x and -99. The greatest common factor of -36x and -99 is -9. Therefore, we write -9 to the left of the top row. You can see it here in the color green:

-9	-36x	-99
11x	44x²	121x
	4x	11

Next, let’s look at the bottom row. We have the terms 44x² and 121x. The greatest common factor of 44x² and 121x is 11x. Therefore, we write 11x to the left of the bottom row. You can see it here in the color blue:

-9	-36x	-99
11x	44x²	121x
	4x	11

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

44x² ÷ 11x = 4x

You can see this value colored in orange below:

-9	-36x	-99
11x	44x²	121x
	4x	11

Next, we divide 121x by 11x (labeled in blue). This gives us 11.

121x ÷ 11x = 11

You can see this value colored in purple below:

-9	-36x	-99
11x	44x²	121x
	4x	11

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 + 85x - 99. 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:

(11x - 9)(4x + 11)

That’s it! Now you know how to factor the equation 44x² + 85x - 99.

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