Factor -34x² - 64x

Factor -34x² - 64x - 30

Here we will show you how to factor the quadratic function -34x² - 64x - 30 using the box method. In other words, we will show you how to factor negative 34x squared minus 64x minus 30 (-34x^2 - 64x - 30) 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 34x² + 64x + 30. Now we can label the different parts of our equation, like this:

a = 34
b = 64
c = 30

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

30	30x	30
34x	34x²	34x
	x	1

We put 34x² (a) in the bottom left square and 30 (c) in the top right square, like this:

30	30x	30
34x	34x²	34x
	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 34 times 30 (a × c), and add together to equal 64 (b).

More specifically, 34 times 30 is 1020. Therefore, we need to find the two numbers that multiply to equal 1020, and add to equal 64.

? × ? = 1020
? + ? = 64

After looking at this problem, we can see that the two numbers that multiply together to equal 1020, and add together to equal 64, are 30 and 34, as illustrated here:

30 × 34 = 1020
30 + 34 = 64

Now, we can fill in the last two squares in our box with 30x and 34x. Place 30x in the upper left square, and place 34x in the lower right square.

30	30x	30
34x	34x²	34x
	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 30x and 30. The greatest common factor of 30x and 30 is 30. Therefore, we write 30 to the left of the top row. You can see it here in the color green:

30	30x	30
34x	34x²	34x
	x	1

Next, let’s look at the bottom row. We have the terms 34x² and 34x. The greatest common factor of 34x² and 34x is 34x. Therefore, we write 34x to the left of the bottom row. You can see it here in the color blue:

30	30x	30
34x	34x²	34x
	x	1

To find the values below the table, we first divide 34x² by 34x (labeled in blue). This gives us x.

34x² ÷ 34x = x

You can see this value colored in orange below:

30	30x	30
34x	34x²	34x
	x	1

Next, we divide 34x by 34x (labeled in blue). This gives us 1.

34x ÷ 34x = 1

You can see this value colored in purple below:

30	30x	30
34x	34x²	34x
	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 -34x² - 64x - 30. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(34x + 30)(x + 1)

In our original quadratic equation, -34x² - 64x - 30, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(34x + 30)(x + 1)

That’s it! Now you know how to factor the equation -34x² - 64x - 30.

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