Factor 95x² - 94x + 15

Here we will show you how to factor the quadratic function 95x² - 94x + 15 using the box method. In other words, we will show you how to factor 95x squared minus 94x plus 15 (95x^2 - 94x + 15) 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 95x² - 94x + 15, like this:

a = 95
b = -94
c = 15

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

-15	-75x	15
19x	95x²	-19x
	5x	-1

We put 95x² (a) in the bottom left square and 15 (c) in the top right square, like this:

-15	-75x	15
19x	95x²	-19x
	5x	-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 95 times 15 (a × c), and add together to equal -94 (b).

More specifically, 95 times 15 is 1425. Therefore, we need to find the two numbers that multiply to equal 1425, and add to equal -94.

? × ? = 1425
? + ? = -94

After looking at this problem, we can see that the two numbers that multiply together to equal 1425, and add together to equal -94, are -75 and -19, as illustrated here:

-75 × -19 = 1425
-75 + -19 = -94

Now, we can fill in the last two squares in our box with -75x and -19x. Place -75x in the upper left square, and place -19x in the lower right square.

-15	-75x	15
19x	95x²	-19x
	5x	-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 -75x and 15. The greatest common factor of -75x and 15 is -15. Therefore, we write -15 to the left of the top row. You can see it here in the color green:

-15	-75x	15
19x	95x²	-19x
	5x	-1

Next, let’s look at the bottom row. We have the terms 95x² and -19x. The greatest common factor of 95x² and -19x is 19x. Therefore, we write 19x to the left of the bottom row. You can see it here in the color blue:

-15	-75x	15
19x	95x²	-19x
	5x	-1

To find the values below the table, we first divide 95x² by 19x (labeled in blue). This gives us 5x.

95x² ÷ 19x = 5x

You can see this value colored in orange below:

-15	-75x	15
19x	95x²	-19x
	5x	-1

Next, we divide -19x by 19x (labeled in blue). This gives us -1.

-19x ÷ 19x = -1

You can see this value colored in purple below:

-15	-75x	15
19x	95x²	-19x
	5x	-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 95x² - 94x + 15. 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:

(19x - 15)(5x - 1)

That’s it! Now you know how to factor the equation 95x² - 94x + 15.

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