(x-5) divided by (x^2+3x-40)

Step-by-step explanation:

Here is your original equation:

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to later):

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that has an exponent of 2. When variables are multiplied, the exponents are added, meaning that . (Or , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

Next, let's look at the factors of 40:

1 and 40   2 and 20   4 and 10   5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in . Therefore, .

Now let's go back to our original equation and substitute our old expression with the new one:

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a .

Therefore, your simplified answer is   !

Here's the whole process:

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4