Factor 89x² + 11x

Factor 89x² + 11x - 100

Here we will show you how to factor the quadratic function 89x² + 11x - 100 using the box method. In other words, we will show you how to factor 89x squared plus 11x minus 100 (89x^2 + 11x - 100) 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 89x² + 11x - 100, like this:

a = 89
b = 11
c = -100

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

-1	-89x	-100
x	89x²	100x
	89x	100

We put 89x² (a) in the bottom left square and -100 (c) in the top right square, like this:

-1	-89x	-100
x	89x²	100x
	89x	100

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 89 times -100 (a × c), and add together to equal 11 (b).

More specifically, 89 times -100 is -8900. Therefore, we need to find the two numbers that multiply to equal -8900, and add to equal 11.

? × ? = -8900
? + ? = 11

After looking at this problem, we can see that the two numbers that multiply together to equal -8900, and add together to equal 11, are -89 and 100, as illustrated here:

-89 × 100 = -8900
-89 + 100 = 11

Now, we can fill in the last two squares in our box with -89x and 100x. Place -89x in the upper left square, and place 100x in the lower right square.

-1	-89x	-100
x	89x²	100x
	89x	100

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 -89x and -100. The greatest common factor of -89x and -100 is -1. Therefore, we write -1 to the left of the top row. You can see it here in the color green:

-1	-89x	-100
x	89x²	100x
	89x	100

Next, let’s look at the bottom row. We have the terms 89x² and 100x. The greatest common factor of 89x² and 100x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

-1	-89x	-100
x	89x²	100x
	89x	100

To find the values below the table, we first divide 89x² by x (labeled in blue). This gives us 89x.

89x² ÷ x = 89x

You can see this value colored in orange below:

-1	-89x	-100
x	89x²	100x
	89x	100

Next, we divide 100x by x (labeled in blue). This gives us 100.

100x ÷ x = 100

You can see this value colored in purple below:

-1	-89x	-100
x	89x²	100x
	89x	100

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 89x² + 11x - 100. 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:

(x - 1)(89x + 100)

That’s it! Now you know how to factor the equation 89x² + 11x - 100.

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