Factor 60x² + 55x

Factor 60x² + 55x - 5

Here we will show you how to factor the quadratic function 60x² + 55x - 5 using the box method. In other words, we will show you how to factor 60x squared plus 55x minus 5 (60x^2 + 55x - 5) 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 60x² + 55x - 5, like this:

a = 60
b = 55
c = -5

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

-5	-5x	-5
60x	60x²	60x
	x	1

We put 60x² (a) in the bottom left square and -5 (c) in the top right square, like this:

-5	-5x	-5
60x	60x²	60x
	x	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 60 times -5 (a × c), and add together to equal 55 (b).

More specifically, 60 times -5 is -300. Therefore, we need to find the two numbers that multiply to equal -300, and add to equal 55.

? × ? = -300
? + ? = 55

After looking at this problem, we can see that the two numbers that multiply together to equal -300, and add together to equal 55, are -5 and 60, as illustrated here:

-5 × 60 = -300
-5 + 60 = 55

Now, we can fill in the last two squares in our box with -5x and 60x. Place -5x in the upper left square, and place 60x in the lower right square.

-5	-5x	-5
60x	60x²	60x
	x	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 -5x and -5. The greatest common factor of -5x and -5 is -5. Therefore, we write -5 to the left of the top row. You can see it here in the color green:

-5	-5x	-5
60x	60x²	60x
	x	1

Next, let’s look at the bottom row. We have the terms 60x² and 60x. The greatest common factor of 60x² and 60x is 60x. Therefore, we write 60x to the left of the bottom row. You can see it here in the color blue:

-5	-5x	-5
60x	60x²	60x
	x	1

To find the values below the table, we first divide 60x² by 60x (labeled in blue). This gives us x.

60x² ÷ 60x = x

You can see this value colored in orange below:

-5	-5x	-5
60x	60x²	60x
	x	1

Next, we divide 60x by 60x (labeled in blue). This gives us 1.

60x ÷ 60x = 1

You can see this value colored in purple below:

-5	-5x	-5
60x	60x²	60x
	x	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 60x² + 55x - 5. 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:

(60x - 5)(x + 1)

That’s it! Now you know how to factor the equation 60x² + 55x - 5.

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