Factor -15x² - 26x

Factor -15x² - 26x - 11

Here we will show you how to factor the quadratic function -15x² - 26x - 11 using the box method. In other words, we will show you how to factor negative 15x squared minus 26x minus 11 (-15x^2 - 26x - 11) 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 15x² + 26x + 11. Now we can label the different parts of our equation, like this:

a = 15
b = 26
c = 11

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

11	11x	11
15x	15x²	15x
	x	1

We put 15x² (a) in the bottom left square and 11 (c) in the top right square, like this:

11	11x	11
15x	15x²	15x
	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 15 times 11 (a × c), and add together to equal 26 (b).

More specifically, 15 times 11 is 165. Therefore, we need to find the two numbers that multiply to equal 165, and add to equal 26.

? × ? = 165
? + ? = 26

After looking at this problem, we can see that the two numbers that multiply together to equal 165, and add together to equal 26, are 11 and 15, as illustrated here:

11 × 15 = 165
11 + 15 = 26

Now, we can fill in the last two squares in our box with 11x and 15x. Place 11x in the upper left square, and place 15x in the lower right square.

11	11x	11
15x	15x²	15x
	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 11x and 11. The greatest common factor of 11x and 11 is 11. Therefore, we write 11 to the left of the top row. You can see it here in the color green:

11	11x	11
15x	15x²	15x
	x	1

Next, let’s look at the bottom row. We have the terms 15x² and 15x. The greatest common factor of 15x² and 15x is 15x. Therefore, we write 15x to the left of the bottom row. You can see it here in the color blue:

11	11x	11
15x	15x²	15x
	x	1

To find the values below the table, we first divide 15x² by 15x (labeled in blue). This gives us x.

15x² ÷ 15x = x

You can see this value colored in orange below:

11	11x	11
15x	15x²	15x
	x	1

Next, we divide 15x by 15x (labeled in blue). This gives us 1.

15x ÷ 15x = 1

You can see this value colored in purple below:

11	11x	11
15x	15x²	15x
	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 -15x² - 26x - 11. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get:

(15x + 11)(x + 1)

In our original quadratic equation, -15x² - 26x - 11, a is negative. Therefore, we need to add a negative (-) sign before our two sets of parentheses, like this:

-(15x + 11)(x + 1)

That’s it! Now you know how to factor the equation -15x² - 26x - 11.

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