Polynomials and Factoring Discussion
Before engaging in the discussion, view the Discussion Guidelines and the Discussion Rubric to ensure that you understand the expectations for this activity. Once you have posted your response, you are also required to respond to at least two other students’ posts. You may want to check back later to respond to your classmates.
1. Create your own question that could appear on the test for this unit. The question can be about adding, subtracting, multiplying, or factoring polynomials. Solve your own problem to make sure that the question has a solution, but do not submit your answer with your test question. Your classmates will be responsible for solving the problem that you make up.
2. What are two pieces of mathematical advice you have for a classmate who’s about to take an assessment on the content you learned in this unit? Think about what types of mistakes are common when adding, subtracting, multiplying, or factoring polynomials.
For your original discussion post, you only need to respond to #1 and #2.
3. View posts from your classmates and choose one to respond to. You will need to solve the test question that your classmate created. Be sure to show all of your work and explain your solution. Do you agree with the mathematical advice that your classmate posted? Why or why not?
4. View responses and comment on the work of another classmate. You may correct any errors that you find, show another way to solve the problem, or provide constructive feedback on the work.
How many terms does it have?, f ( x ) = x 2 + 5 x + 6
First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.
1. Test Question: Add the polynomials (2x^3 - 4x^2 + 3x + 6) and (-3x^3 + 5x^2 - 2x - 4).
2. Mathematical Advice: When adding or subtracting polynomials, make sure to align the like terms before combining them. It's also important to double check signs, especially when subtracting a polynomial. When multiplying polynomials, use the distributive property to ensure that each term is multiplied by every term in the other polynomial.
Response: To add the polynomials (2x^3 - 4x^2 + 3x + 6) and (-3x^3 + 5x^2 - 2x - 4), we first align the like terms:
2x^3 - 4x^2 + 3x + 6
+ (-3x^3 + 5x^2 - 2x - 4)
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-x^3 + x^2 + x + 2
So, the sum of the two polynomials is -x^3 + x^2 + x + 2.
I agree with the mathematical advice provided, especially the tip about aligning the like terms before combining them. This makes the process much easier and reduces the chances of making mistakes.