Factor 44x² + 70x + 26

Here we will show you how to factor the quadratic function 44x² + 70x + 26 using the box method. In other words, we will show you how to factor 44x squared plus 70x plus 26 (44x^2 + 70x + 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 44x² + 70x + 26, like this:

a = 44
b = 70
c = 26

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

26	26x	26
44x	44x²	44x
	x	1

We put 44x² (a) in the bottom left square and 26 (c) in the top right square, like this:

26	26x	26
44x	44x²	44x
	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 44 times 26 (a × c), and add together to equal 70 (b).

More specifically, 44 times 26 is 1144. Therefore, we need to find the two numbers that multiply to equal 1144, and add to equal 70.

? × ? = 1144
? + ? = 70

After looking at this problem, we can see that the two numbers that multiply together to equal 1144, and add together to equal 70, are 26 and 44, as illustrated here:

26 × 44 = 1144
26 + 44 = 70

Now, we can fill in the last two squares in our box with 26x and 44x. Place 26x in the upper left square, and place 44x in the lower right square.

26	26x	26
44x	44x²	44x
	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 26x and 26. The greatest common factor of 26x and 26 is 26. Therefore, we write 26 to the left of the top row. You can see it here in the color green:

26	26x	26
44x	44x²	44x
	x	1

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

26	26x	26
44x	44x²	44x
	x	1

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

44x² ÷ 44x = x

You can see this value colored in orange below:

26	26x	26
44x	44x²	44x
	x	1

Next, we divide 44x by 44x (labeled in blue). This gives us 1.

44x ÷ 44x = 1

You can see this value colored in purple below:

26	26x	26
44x	44x²	44x
	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 44x² + 70x + 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:

(44x + 26)(x + 1)

That’s it! Now you know how to factor the equation 44x² + 70x + 26.

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