Weekly Math Problem! #35

Polynomial Division. Alright folks. I think I've mentioned this before but, I'm not sure. So, I am mentioning it now. I do my best to make sure I am mixing up the type of problems I post every week. I have learned different types and levels of math over the years and have liked most of it. (Although, I possess a bias for calculus.) As a tutor, I want to make sure that I can help others with various levels of math, especially at the college level. One of the things I have to consider when choosing a problem is making sure that I am able to type the question and it's solution. This week's problem is good. 👍🏿 (I don't know if that's a hint or not. 🤷🏿‍♀️)

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to divide a polynomial by a binomial

Ready? Great! WMP! #35 says:

Happy solving!

Check back on Friday, January 29th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Jumping right in, the numerator in the problem (which is also the dividend) is prime--it cannot be factored. Since, it cannot be factored and reduced, this division needs to be completed the long way...literally ---> via long division. 🥴 Sorry...

Unfortunately, I couldn't show each individual step of the long division process. (A video is needed for that.) What I've done, instead, is just showed the completed long division in two forms--the first with the undistributed negative sign and the second with the distributed negative sign. **Notice that the dividend lacks a cubic term. So, to proceed with the long division method, a place holder must be used:  0x3 

 

    

As you can see there is a reminder. The reminder should be written as a fraction, with the divisor as the denominator. Putting that along with the quotient shows the final answer as follows: 

Wait...not so fast. Let's check it! (That's one of the things that I like about math--you can check your work). To check, we'll multiply the quotient and the divisor, adding the reminder to it.

Now, you're free to go. The check works out and I am satisfied. 

▪️ Did your solution work out?

▪️ Leave your response down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Onward to WMP! #36

Cheers!

The Younge Lady