Factor -24x² - 50x

Factor -24x² - 50x - 14

Here we will show you how to factor the quadratic function -24x² - 50x - 14 using the box method. In other words, we will show you how to factor negative 24x squared minus 50x minus 14 (-24x^2 - 50x - 14) 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 24x² + 50x + 14. Now we can label the different parts of our equation, like this:

a = 24
b = 50
c = 14

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

2	8x	14
6x	24x²	42x
	4x	7

We put 24x² (a) in the bottom left square and 14 (c) in the top right square, like this:

2	8x	14
6x	24x²	42x
	4x	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 24 times 14 (a × c), and add together to equal 50 (b).

More specifically, 24 times 14 is 336. Therefore, we need to find the two numbers that multiply to equal 336, and add to equal 50.

? × ? = 336
? + ? = 50

After looking at this problem, we can see that the two numbers that multiply together to equal 336, and add together to equal 50, are 8 and 42, as illustrated here:

8 × 42 = 336
8 + 42 = 50

Now, we can fill in the last two squares in our box with 8x and 42x. Place 8x in the upper left square, and place 42x in the lower right square.

2	8x	14
6x	24x²	42x
	4x	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 8x and 14. The greatest common factor of 8x and 14 is 2. Therefore, we write 2 to the left of the top row. You can see it here in the color green:

2	8x	14
6x	24x²	42x
	4x	7

Next, let’s look at the bottom row. We have the terms 24x² and 42x. The greatest common factor of 24x² and 42x is 6x. Therefore, we write 6x to the left of the bottom row. You can see it here in the color blue:

2	8x	14
6x	24x²	42x
	4x	7

To find the values below the table, we first divide 24x² by 6x (labeled in blue). This gives us 4x.

24x² ÷ 6x = 4x

You can see this value colored in orange below:

2	8x	14
6x	24x²	42x
	4x	7

Next, we divide 42x by 6x (labeled in blue). This gives us 7.

42x ÷ 6x = 7

You can see this value colored in purple below:

2	8x	14
6x	24x²	42x
	4x	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 -24x² - 50x - 14. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(6x + 2)(4x + 7)

In our original quadratic equation, -24x² - 50x - 14, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(6x + 2)(4x + 7)

That’s it! Now you know how to factor the equation -24x² - 50x - 14.

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