Factor 15x² + 64x + 57


Factoring Quadratics

Here we will show you how to factor the quadratic function 15x² + 64x + 57 using the box method. In other words, we will show you how to factor 15x squared plus 64x plus 57 (15x^2 + 64x + 57) 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 + 64x + 57, like this:

a = 15
b = 64
c = 57


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

19  19x 57
15x  15x² 45x
x 3
We put 15x² (a) in the bottom left square and 57 (c) in the top right square, like this:

19  19x 57
15x  15x² 45x
x 3
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 57 (a × c), and add together to equal 64 (b).

More specifically, 15 times 57 is 855. Therefore, we need to find the two numbers that multiply to equal 855, and add to equal 64.

? × ? = 855
? + ? = 64

After looking at this problem, we can see that the two numbers that multiply together to equal 855, and add together to equal 64, are 19 and 45, as illustrated here:

19 × 45 = 855
19 + 45 = 64

Now, we can fill in the last two squares in our box with 19x and 45x. Place 19x in the upper left square, and place 45x in the lower right square.

19  19x 57
15x  15x² 45x
x 3
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 19x and 57. The greatest common factor of 19x and 57 is 19. Therefore, we write 19 to the left of the top row. You can see it here in the color green:

19  19x 57
15x  15x² 45x
x 3
Next, let’s look at the bottom row. We have the terms 15x² and 45x. The greatest common factor of 15x² and 45x is 15x. Therefore, we write 15x to the left of the bottom row. You can see it here in the color blue:

19  19x 57
15x  15x² 45x
x 3
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:

19  19x 57
15x  15x² 45x
x 3

Next, we divide 45x by 15x (labeled in blue). This gives us 3.

45x ÷ 15x = 3

You can see this value colored in purple below:

19  19x 57
15x  15x² 45x
x 3

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 + 64x + 57. 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:

(15x + 19)(x + 3)

That’s it! Now you know how to factor the equation 15x² + 64x + 57.


Factoring Quadratics
Go here if you want to learn how to factor another quadratic function.

Factor 15x² + 64x + 64
Here is the next quadratic function on our list that we have factored for you.


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