Factor 60x² + 56x

Factor 60x² + 56x - 43

Here we will show you how to factor the quadratic function 60x² + 56x - 43 using the box method. In other words, we will show you how to factor 60x squared plus 56x minus 43 (60x^2 + 56x - 43) 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 + 56x - 43, like this:

a = 60
b = 56
c = -43

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

-1	-30x	-43
2x	60x²	86x
	30x	43

We put 60x² (a) in the bottom left square and -43 (c) in the top right square, like this:

-1	-30x	-43
2x	60x²	86x
	30x	43

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 -43 (a × c), and add together to equal 56 (b).

More specifically, 60 times -43 is -2580. Therefore, we need to find the two numbers that multiply to equal -2580, and add to equal 56.

? × ? = -2580
? + ? = 56

After looking at this problem, we can see that the two numbers that multiply together to equal -2580, and add together to equal 56, are -30 and 86, as illustrated here:

-30 × 86 = -2580
-30 + 86 = 56

Now, we can fill in the last two squares in our box with -30x and 86x. Place -30x in the upper left square, and place 86x in the lower right square.

-1	-30x	-43
2x	60x²	86x
	30x	43

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 -30x and -43. The greatest common factor of -30x and -43 is -1. Therefore, we write -1 to the left of the top row. You can see it here in the color green:

-1	-30x	-43
2x	60x²	86x
	30x	43

Next, let’s look at the bottom row. We have the terms 60x² and 86x. The greatest common factor of 60x² and 86x is 2x. Therefore, we write 2x to the left of the bottom row. You can see it here in the color blue:

-1	-30x	-43
2x	60x²	86x
	30x	43

To find the values below the table, we first divide 60x² by 2x (labeled in blue). This gives us 30x.

60x² ÷ 2x = 30x

You can see this value colored in orange below:

-1	-30x	-43
2x	60x²	86x
	30x	43

Next, we divide 86x by 2x (labeled in blue). This gives us 43.

86x ÷ 2x = 43

You can see this value colored in purple below:

-1	-30x	-43
2x	60x²	86x
	30x	43

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 + 56x - 43. 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:

(2x - 1)(30x + 43)

That’s it! Now you know how to factor the equation 60x² + 56x - 43.

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