Factor 26x² + 99x + 94

Here we will show you how to factor the quadratic function 26x² + 99x + 94 using the box method. In other words, we will show you how to factor 26x squared plus 99x plus 94 (26x^2 + 99x + 94) 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 26x² + 99x + 94, like this:

a = 26
b = 99
c = 94

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

47	47x	94
26x	26x²	52x
	x	2

We put 26x² (a) in the bottom left square and 94 (c) in the top right square, like this:

47	47x	94
26x	26x²	52x
	x	2

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 26 times 94 (a × c), and add together to equal 99 (b).

More specifically, 26 times 94 is 2444. Therefore, we need to find the two numbers that multiply to equal 2444, and add to equal 99.

? × ? = 2444
? + ? = 99

After looking at this problem, we can see that the two numbers that multiply together to equal 2444, and add together to equal 99, are 47 and 52, as illustrated here:

47 × 52 = 2444
47 + 52 = 99

Now, we can fill in the last two squares in our box with 47x and 52x. Place 47x in the upper left square, and place 52x in the lower right square.

47	47x	94
26x	26x²	52x
	x	2

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 47x and 94. The greatest common factor of 47x and 94 is 47. Therefore, we write 47 to the left of the top row. You can see it here in the color green:

47	47x	94
26x	26x²	52x
	x	2

Next, let’s look at the bottom row. We have the terms 26x² and 52x. The greatest common factor of 26x² and 52x is 26x. Therefore, we write 26x to the left of the bottom row. You can see it here in the color blue:

47	47x	94
26x	26x²	52x
	x	2

To find the values below the table, we first divide 26x² by 26x (labeled in blue). This gives us x.

26x² ÷ 26x = x

You can see this value colored in orange below:

47	47x	94
26x	26x²	52x
	x	2

Next, we divide 52x by 26x (labeled in blue). This gives us 2.

52x ÷ 26x = 2

You can see this value colored in purple below:

47	47x	94
26x	26x²	52x
	x	2

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 26x² + 99x + 94. 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:

(26x + 47)(x + 2)

That’s it! Now you know how to factor the equation 26x² + 99x + 94.

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