M5D1: Factoring
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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.
(NOTE***Complete the questions attached )using the directions