Factor 10x² + 91x + 88

Here we will show you how to factor the quadratic function 10x² + 91x + 88 using the box method. In other words, we will show you how to factor 10x squared plus 91x plus 88 (10x^2 + 91x + 88) 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 10x² + 91x + 88, like this:

a = 10
b = 91
c = 88

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

11	11x	88
10x	10x²	80x
	x	8

We put 10x² (a) in the bottom left square and 88 (c) in the top right square, like this:

11	11x	88
10x	10x²	80x
	x	8

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 10 times 88 (a × c), and add together to equal 91 (b).

More specifically, 10 times 88 is 880. Therefore, we need to find the two numbers that multiply to equal 880, and add to equal 91.

? × ? = 880
? + ? = 91

After looking at this problem, we can see that the two numbers that multiply together to equal 880, and add together to equal 91, are 11 and 80, as illustrated here:

11 × 80 = 880
11 + 80 = 91

Now, we can fill in the last two squares in our box with 11x and 80x. Place 11x in the upper left square, and place 80x in the lower right square.

11	11x	88
10x	10x²	80x
	x	8

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 11x and 88. The greatest common factor of 11x and 88 is 11. Therefore, we write 11 to the left of the top row. You can see it here in the color green:

11	11x	88
10x	10x²	80x
	x	8

Next, let’s look at the bottom row. We have the terms 10x² and 80x. The greatest common factor of 10x² and 80x is 10x. Therefore, we write 10x to the left of the bottom row. You can see it here in the color blue:

11	11x	88
10x	10x²	80x
	x	8

To find the values below the table, we first divide 10x² by 10x (labeled in blue). This gives us x.

10x² ÷ 10x = x

You can see this value colored in orange below:

11	11x	88
10x	10x²	80x
	x	8

Next, we divide 80x by 10x (labeled in blue). This gives us 8.

80x ÷ 10x = 8

You can see this value colored in purple below:

11	11x	88
10x	10x²	80x
	x	8

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 10x² + 91x + 88. 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:

(10x + 11)(x + 8)

That’s it! Now you know how to factor the equation 10x² + 91x + 88.

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