Factor 15x² + 62x + 64

Here we will show you how to factor the quadratic function 15x² + 62x + 64 using the box method. In other words, we will show you how to factor 15x squared plus 62x plus 64 (15x^2 + 62x + 64) 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 15x² + 62x + 64, like this:

a = 15
b = 62
c = 64

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

2	30x	64
x	15x²	32x
	15x	32

We put 15x² (a) in the bottom left square and 64 (c) in the top right square, like this:

2	30x	64
x	15x²	32x
	15x	32

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 64 (a × c), and add together to equal 62 (b).

More specifically, 15 times 64 is 960. Therefore, we need to find the two numbers that multiply to equal 960, and add to equal 62.

? × ? = 960
? + ? = 62

After looking at this problem, we can see that the two numbers that multiply together to equal 960, and add together to equal 62, are 30 and 32, as illustrated here:

30 × 32 = 960
30 + 32 = 62

Now, we can fill in the last two squares in our box with 30x and 32x. Place 30x in the upper left square, and place 32x in the lower right square.

2	30x	64
x	15x²	32x
	15x	32

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 64. The greatest common factor of 30x and 64 is 2. Therefore, we write 2 to the left of the top row. You can see it here in the color green:

2	30x	64
x	15x²	32x
	15x	32

Next, let’s look at the bottom row. We have the terms 15x² and 32x. The greatest common factor of 15x² and 32x is x. Therefore, we write x to the left of the bottom row. You can see it here in the color blue:

2	30x	64
x	15x²	32x
	15x	32

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

15x² ÷ x = 15x

You can see this value colored in orange below:

2	30x	64
x	15x²	32x
	15x	32

Next, we divide 32x by x (labeled in blue). This gives us 32.

32x ÷ x = 32

You can see this value colored in purple below:

2	30x	64
x	15x²	32x
	15x	32

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 + 62x + 64. 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:

(x + 2)(15x + 32)

That’s it! Now you know how to factor the equation 15x² + 62x + 64.

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