Factor 24x² + 17x

Factor 24x² + 17x - 95

Here we will show you how to factor the quadratic function 24x² + 17x - 95 using the box method. In other words, we will show you how to factor 24x squared plus 17x minus 95 (24x^2 + 17x - 95) 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 24x² + 17x - 95, like this:

a = 24
b = 17
c = -95

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

-5	-40x	-95
3x	24x²	57x
	8x	19

We put 24x² (a) in the bottom left square and -95 (c) in the top right square, like this:

-5	-40x	-95
3x	24x²	57x
	8x	19

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 -95 (a × c), and add together to equal 17 (b).

More specifically, 24 times -95 is -2280. Therefore, we need to find the two numbers that multiply to equal -2280, and add to equal 17.

? × ? = -2280
? + ? = 17

After looking at this problem, we can see that the two numbers that multiply together to equal -2280, and add together to equal 17, are -40 and 57, as illustrated here:

-40 × 57 = -2280
-40 + 57 = 17

Now, we can fill in the last two squares in our box with -40x and 57x. Place -40x in the upper left square, and place 57x in the lower right square.

-5	-40x	-95
3x	24x²	57x
	8x	19

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 -40x and -95. The greatest common factor of -40x and -95 is -5. Therefore, we write -5 to the left of the top row. You can see it here in the color green:

-5	-40x	-95
3x	24x²	57x
	8x	19

Next, let’s look at the bottom row. We have the terms 24x² and 57x. The greatest common factor of 24x² and 57x is 3x. Therefore, we write 3x to the left of the bottom row. You can see it here in the color blue:

-5	-40x	-95
3x	24x²	57x
	8x	19

To find the values below the table, we first divide 24x² by 3x (labeled in blue). This gives us 8x.

24x² ÷ 3x = 8x

You can see this value colored in orange below:

-5	-40x	-95
3x	24x²	57x
	8x	19

Next, we divide 57x by 3x (labeled in blue). This gives us 19.

57x ÷ 3x = 19

You can see this value colored in purple below:

-5	-40x	-95
3x	24x²	57x
	8x	19

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 + 17x - 95. 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:

(3x - 5)(8x + 19)

That’s it! Now you know how to factor the equation 24x² + 17x - 95.

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