Factor 21x² + 47x + 26

Here we will show you how to factor the quadratic function 21x² + 47x + 26 using the box method. In other words, we will show you how to factor 21x squared plus 47x plus 26 (21x^2 + 47x + 26) 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 21x² + 47x + 26, like this:

a = 21
b = 47
c = 26

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

1	21x	26
x	21x²	26x
	21x	26

We put 21x² (a) in the bottom left square and 26 (c) in the top right square, like this:

1	21x	26
x	21x²	26x
	21x	26

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 21 times 26 (a × c), and add together to equal 47 (b).

More specifically, 21 times 26 is 546. Therefore, we need to find the two numbers that multiply to equal 546, and add to equal 47.

? × ? = 546
? + ? = 47

After looking at this problem, we can see that the two numbers that multiply together to equal 546, and add together to equal 47, are 21 and 26, as illustrated here:

21 × 26 = 546
21 + 26 = 47

Now, we can fill in the last two squares in our box with 21x and 26x. Place 21x in the upper left square, and place 26x in the lower right square.

1	21x	26
x	21x²	26x
	21x	26

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 21x and 26. The greatest common factor of 21x and 26 is 1. Therefore, we write 1 to the left of the top row. You can see it here in the color green:

1	21x	26
x	21x²	26x
	21x	26

Next, let’s look at the bottom row. We have the terms 21x² and 26x. The greatest common factor of 21x² and 26x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

1	21x	26
x	21x²	26x
	21x	26

To find the values below the table, we first divide 21x² by x (labeled in blue). This gives us 21x.

21x² ÷ x = 21x

You can see this value colored in orange below:

1	21x	26
x	21x²	26x
	21x	26

Next, we divide 26x by x (labeled in blue). This gives us 26.

26x ÷ x = 26

You can see this value colored in purple below:

1	21x	26
x	21x²	26x
	21x	26

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 21x² + 47x + 26. 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)(21x + 26)

That’s it! Now you know how to factor the equation 21x² + 47x + 26.

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