Factor 44x² + 80x + 29

Here we will show you how to factor the quadratic function 44x² + 80x + 29 using the box method. In other words, we will show you how to factor 44x squared plus 80x plus 29 (44x^2 + 80x + 29) 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 44x² + 80x + 29, like this:

a = 44
b = 80
c = 29

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

1	22x	29
2x	44x²	58x
	22x	29

We put 44x² (a) in the bottom left square and 29 (c) in the top right square, like this:

1	22x	29
2x	44x²	58x
	22x	29

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 44 times 29 (a × c), and add together to equal 80 (b).

More specifically, 44 times 29 is 1276. Therefore, we need to find the two numbers that multiply to equal 1276, and add to equal 80.

? × ? = 1276
? + ? = 80

After looking at this problem, we can see that the two numbers that multiply together to equal 1276, and add together to equal 80, are 22 and 58, as illustrated here:

22 × 58 = 1276
22 + 58 = 80

Now, we can fill in the last two squares in our box with 22x and 58x. Place 22x in the upper left square, and place 58x in the lower right square.

1	22x	29
2x	44x²	58x
	22x	29

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 22x and 29. The greatest common factor of 22x and 29 is 1. Therefore, we write 1 to the left of the top row. You can see it here in the color green:

1	22x	29
2x	44x²	58x
	22x	29

Next, let’s look at the bottom row. We have the terms 44x² and 58x. The greatest common factor of 44x² and 58x is 2x. Therefore, we write 2x to the left of the bottom row. You can see it here in the color blue:

1	22x	29
2x	44x²	58x
	22x	29

To find the values below the table, we first divide 44x² by 2x (labeled in blue). This gives us 22x.

44x² ÷ 2x = 22x

You can see this value colored in orange below:

1	22x	29
2x	44x²	58x
	22x	29

Next, we divide 58x by 2x (labeled in blue). This gives us 29.

58x ÷ 2x = 29

You can see this value colored in purple below:

1	22x	29
2x	44x²	58x
	22x	29

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 44x² + 80x + 29. 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)(22x + 29)

That’s it! Now you know how to factor the equation 44x² + 80x + 29.

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