Factor 20x² + 96x + 43

Here we will show you how to factor the quadratic function 20x² + 96x + 43 using the box method. In other words, we will show you how to factor 20x squared plus 96x plus 43 (20x^2 + 96x + 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 20x² + 96x + 43, like this:

a = 20
b = 96
c = 43

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

1	10x	43
2x	20x²	86x
	10x	43

We put 20x² (a) in the bottom left square and 43 (c) in the top right square, like this:

1	10x	43
2x	20x²	86x
	10x	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 20 times 43 (a × c), and add together to equal 96 (b).

More specifically, 20 times 43 is 860. Therefore, we need to find the two numbers that multiply to equal 860, and add to equal 96.

? × ? = 860
? + ? = 96

After looking at this problem, we can see that the two numbers that multiply together to equal 860, and add together to equal 96, are 10 and 86, as illustrated here:

10 × 86 = 860
10 + 86 = 96

Now, we can fill in the last two squares in our box with 10x and 86x. Place 10x in the upper left square, and place 86x in the lower right square.

1	10x	43
2x	20x²	86x
	10x	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 10x and 43. The greatest common factor of 10x 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	10x	43
2x	20x²	86x
	10x	43

Next, let’s look at the bottom row. We have the terms 20x² and 86x. The greatest common factor of 20x² 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	10x	43
2x	20x²	86x
	10x	43

To find the values below the table, we first divide 20x² by 2x (labeled in blue). This gives us 10x.

20x² ÷ 2x = 10x

You can see this value colored in orange below:

1	10x	43
2x	20x²	86x
	10x	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	10x	43
2x	20x²	86x
	10x	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 20x² + 96x + 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)(10x + 43)

That’s it! Now you know how to factor the equation 20x² + 96x + 43.

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