Factor 87x² + 100x + 28

Here we will show you how to factor the quadratic function 87x² + 100x + 28 using the box method. In other words, we will show you how to factor 87x squared plus 100x plus 28 (87x^2 + 100x + 28) 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 87x² + 100x + 28, like this:

a = 87
b = 100
c = 28

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

14	42x	28
29x	87x²	58x
	3x	2

We put 87x² (a) in the bottom left square and 28 (c) in the top right square, like this:

14	42x	28
29x	87x²	58x
	3x	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 87 times 28 (a × c), and add together to equal 100 (b).

More specifically, 87 times 28 is 2436. Therefore, we need to find the two numbers that multiply to equal 2436, and add to equal 100.

? × ? = 2436
? + ? = 100

After looking at this problem, we can see that the two numbers that multiply together to equal 2436, and add together to equal 100, are 42 and 58, as illustrated here:

42 × 58 = 2436
42 + 58 = 100

Now, we can fill in the last two squares in our box with 42x and 58x. Place 42x in the upper left square, and place 58x in the lower right square.

14	42x	28
29x	87x²	58x
	3x	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 42x and 28. The greatest common factor of 42x and 28 is 14. Therefore, we write 14 to the left of the top row. You can see it here in the color green:

14	42x	28
29x	87x²	58x
	3x	2

Next, let’s look at the bottom row. We have the terms 87x² and 58x. The greatest common factor of 87x² and 58x is 29x. Therefore, we write 29x to the left of the bottom row. You can see it here in the color blue:

14	42x	28
29x	87x²	58x
	3x	2

To find the values below the table, we first divide 87x² by 29x (labeled in blue). This gives us 3x.

87x² ÷ 29x = 3x

You can see this value colored in orange below:

14	42x	28
29x	87x²	58x
	3x	2

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

58x ÷ 29x = 2

You can see this value colored in purple below:

14	42x	28
29x	87x²	58x
	3x	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 87x² + 100x + 28. 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:

(29x + 14)(3x + 2)

That’s it! Now you know how to factor the equation 87x² + 100x + 28.

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