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.
1. On a test, John is asked to factor the polynomial expression 3x^2 + 10x + 3. John correctly factors the trinomial into (3x + 1)(x + 3) and states that these are the two factors of the polynomial. However, his classmate points out that there is another correct factorization. Can you find the correct factorization for the given polynomial expression?
2. Two pieces of mathematical advice that I have for a classmate who's about to take an assessment on adding, subtracting, multiplying, or factoring polynomials are:
a) Pay attention to signs: One common mistake students make is neglecting to properly distribute the negative sign when subtracting or multiplying polynomials. Always double-check the signs and be mindful of positive and negative numbers.
b) Double-check your solutions: When factoring polynomials, it's important to verify that the factors multiplied together actually give back the original expression. This can be easily done by multiplying the factors back together to ensure they equal the original polynomial. This step helps to catch any errors made in the factorization process.