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Factoring a trinomial Expression a x squared + b x + c. Step 1. Write all pairs of factors of a x squared. Step 2. Write all pairs of factors of c, the constant. Step 3. Try all combinations of above factors to find the ones that lead to b x squared. Step 4. If no such combination exists, the polynomial is prime. An example is given: 6 x squared + 13 x 5 = 3 x minus 1 times 2 x + 5.Factoring is a skill that is important in simplifying expressions, solving equations, and in many applications. Therefore, it is important that you practice this skill so you can use it when the need arises. One reason it takes some practice is because the method used depends on the precise type of expression you are trying to factor.
Our main focus in this activity and in this module is factoring a trinomial expression of the form ax2 + bx + c and solving the related trinomial equation, ax2 + bx + c = 0. There are two main techniques used to factor these, depending on whether the coefficient a of the leading term ax2 is 1, the simpler case, or if a is some real number other than 1. These techniques are covered on in Section 5.5 of your textbook.
But we are also considering the special case binomials called the difference of squares and the sum and difference of cubes. These special cases have their own factoring strategies, as outlined in your textbook in Section 5.6.
Keep in mind that, for any given trinomial you will encounter in this module, it may or may not be factorable. To prove that ax2 + bx + c is not factorable, for this class it is sufficient to show that the appropriate factoring techniques covered in Sections 5.5-5.6 do not work.
Let’s begin our discussion:
Without looking at any factoring problems in the book, please do the following:
Create 2 polynomial expressions that are factorable. Here are important guidelines:
Your polynomial must be at least of order 2 i.e., have an x2 term or higher)
If you create a quadratic (ax2 + bx + c) you must choose a 1.
If you create a cubic that can be factored using the sum and difference of cubes, you will get 2 extra points.
Remember that factoring is the inverse operation of multiplication of polynomials. This hint should be useful when creating your problems and checking your work.
Create 1 polynomial expression that is not factorable.
You may put the 3 expressions in any order.
To complete the discussion: Thoroughly complete the directions listed above. To gain full credit, you must reply to the posts of at least two classmates. Also, return to your original post throughout the week to read and reply to any posts made there by others. In the two reply posts to your classmates, do one of the following:
Work with the expressions of one of your classmates:
Show your steps when factoring the two factorable expressions posted by a classmate. Check your factorization by multiplying together the factors you obtain and verify that you get back the expression you started with.
Prove that the other expression posted by this classmate is not factorable, i.e., show that the appropriate factoring techniques covered in Sections 5.55.6 do not work for this expression.
Point out an error in someone elses work and provide a correction. In this case, try to include a tip that might help avoid such mistakes.
As one of your replies, you may ask a question about these factoring techniques to help you understand, or pass along a tip to a classmate that might help him/her.
Unless you are pointing out an error, try to choose the expressions that have not already been solved by someone else.
Your initial post is due by Thursday at 11:59 PM. Your responses are due by Sunday at 11:59 PM