Factor 17x² + 33x

Factor 17x² + 33x - 50

Here we will show you how to factor the quadratic function 17x² + 33x - 50 using the box method. In other words, we will show you how to factor 17x squared plus 33x minus 50 (17x^2 + 33x - 50) 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 17x² + 33x - 50, like this:

a = 17
b = 33
c = -50

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

-1	-17x	-50
x	17x²	50x
	17x	50

We put 17x² (a) in the bottom left square and -50 (c) in the top right square, like this:

-1	-17x	-50
x	17x²	50x
	17x	50

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 17 times -50 (a × c), and add together to equal 33 (b).

More specifically, 17 times -50 is -850. Therefore, we need to find the two numbers that multiply to equal -850, and add to equal 33.

? × ? = -850
? + ? = 33

After looking at this problem, we can see that the two numbers that multiply together to equal -850, and add together to equal 33, are -17 and 50, as illustrated here:

-17 × 50 = -850
-17 + 50 = 33

Now, we can fill in the last two squares in our box with -17x and 50x. Place -17x in the upper left square, and place 50x in the lower right square.

-1	-17x	-50
x	17x²	50x
	17x	50

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 -17x and -50. The greatest common factor of -17x and -50 is -1. Therefore, we write -1 to the left of the top row. You can see it here in the color green:

-1	-17x	-50
x	17x²	50x
	17x	50

Next, let’s look at the bottom row. We have the terms 17x² and 50x. The greatest common factor of 17x² and 50x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

-1	-17x	-50
x	17x²	50x
	17x	50

To find the values below the table, we first divide 17x² by x (labeled in blue). This gives us 17x.

17x² ÷ x = 17x

You can see this value colored in orange below:

-1	-17x	-50
x	17x²	50x
	17x	50

Next, we divide 50x by x (labeled in blue). This gives us 50.

50x ÷ x = 50

You can see this value colored in purple below:

-1	-17x	-50
x	17x²	50x
	17x	50

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 17x² + 33x - 50. 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)(17x + 50)

That’s it! Now you know how to factor the equation 17x² + 33x - 50.

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