Factor -8x² - 70x

Factor -8x² - 70x - 98

Here we will show you how to factor the quadratic function -8x² - 70x - 98 using the box method. In other words, we will show you how to factor negative 8x squared minus 70x minus 98 (-8x^2 - 70x - 98) using the box method. It is a 5-step process:

Step 1: The standard form of a quadratic equation is ax² + bx + c. In this equation, a is negative. Therefore, we need to start by setting aside the negative (-). We do this by flipping the signs in the equation to get 8x² + 70x + 98. Now we can label the different parts of our equation, like this:

a = 8
b = 70
c = 98

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

14	14x	98
8x	8x²	56x
	x	7

We put 8x² (a) in the bottom left square and 98 (c) in the top right square, like this:

14	14x	98
8x	8x²	56x
	x	7

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 8 times 98 (a × c), and add together to equal 70 (b).

More specifically, 8 times 98 is 784. Therefore, we need to find the two numbers that multiply to equal 784, and add to equal 70.

? × ? = 784
? + ? = 70

After looking at this problem, we can see that the two numbers that multiply together to equal 784, and add together to equal 70, are 14 and 56, as illustrated here:

14 × 56 = 784
14 + 56 = 70

Now, we can fill in the last two squares in our box with 14x and 56x. Place 14x in the upper left square, and place 56x in the lower right square.

14	14x	98
8x	8x²	56x
	x	7

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 14x and 98. The greatest common factor of 14x and 98 is 14. Therefore, we write 14 to the left of the top row. You can see it here in the color green:

14	14x	98
8x	8x²	56x
	x	7

Next, let’s look at the bottom row. We have the terms 8x² and 56x. The greatest common factor of 8x² and 56x is 8x. Therefore, we write 8x to the left of the bottom row. You can see it here in the color blue:

14	14x	98
8x	8x²	56x
	x	7

To find the values below the table, we first divide 8x² by 8x (labeled in blue). This gives us x.

8x² ÷ 8x = x

You can see this value colored in orange below:

14	14x	98
8x	8x²	56x
	x	7

Next, we divide 56x by 8x (labeled in blue). This gives us 7.

56x ÷ 8x = 7

You can see this value colored in purple below:

14	14x	98
8x	8x²	56x
	x	7

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 -8x² - 70x - 98. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(8x + 14)(x + 7)

In our original quadratic equation, -8x² - 70x - 98, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(8x + 14)(x + 7)

That’s it! Now you know how to factor the equation -8x² - 70x - 98.

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