7.3 Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c

Having learned about the basics of the Polynomials, Operations of polynomials, and Prime factorization in previous chapters, we are now more equipped to proceed to a more complex concept. In this chapter we will proceed to learning about factoring polynomial expressions.

Polynomials can be factored by looking at the common factors. So if we are given 15x4+3x3+x215x^4 + 3x^3 + x^2, using the knowledge we have about factoring we can be able to deduce that the common factor for each term in this expression is x2x^2, thus the remaining part of the equation will be (15x2+3x+115x^2 + 3x + 1) which can be factored out again.

Factoring can also be done by grouping the polynomials. This would test our understanding of the FOIL method which we use in multiplying one polynomial to another. So if we are given an expression 3x + 7y – 21 – xy, we would get the factors, (3-y) and (x-7) by grouping (3x- xy) and (7y-21). We could always counter check the answers by applying the FOIL method.

In the proceeding parts of the chapter, after looking at the different ways to factor polynomial expressions, we will then look at the polynomial expressions: x2+bx+cx^2 + bx +c, and ax2+bx+cax^2 + bx +c (the quadratic equation). We are going to learn how to factor these two expressions and also solve for b and c. There are also a number of applications for these two forms of polynomial equations so we would look into that as well.

We will be slightly talking about special products since Perfect Square Trinomials and Difference of Squares will also be tackled, specifically on how these should be factored. After we learn all of the basics about factoring polynomials, we will be answering exercises to test our understanding.

Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c

In this lesson, we will be doing trinomial factoring to find all possible answers for the unknowns in the term in the middle of the polynomials. By doing so, we will need to reverse the process of FOIL so that we can convert the trinomials into two binomials.


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Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c

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