There are several of ways as to solving polynomial equations. One of the ways is to use factors, another way is factoring, and lastly, by graphing.
Factoring: is rewriting an expression as the product of its factors.
To solve by using factors you are finding the real/imaginary solutions to the equation.
Example:
An easy step by step method of memorizing how to factor is:
1.) a * c =
2.) find the number that multiply to c, and add to b
3.) then rewrite using the new terms
4.) then combine the first two terms and the last two terms together and GCF
5.) then combine like terms to simplify
An example following these steps:
4x2 – 4x - 3
1.) a * c 2.) multiply to c add to b 3.) rewrite using new terms 4.) then GCF 5.) then combine like terms | 1.) 4 * -3 = -12 2.) -6 , 2
3.) 4x2 + 2x - 6x - 3 4.) 2x ( 2x + 1 ) - 3 (2x + 1) 5.) (2x - 3) (2x + 1) - final answer |
There are different ways to factor, below the chart shows you many ways that you can use to help factor out the polynomial.
Not only is there factoring to solve the polynomials but there is graphing to solve. When graphing you are looking for the zeroes in the graphing calculator's table. An example of how to solve by graphing is shown below.
Writing a Polynomial from Factors:
Ex.)
Write a polynomial function from the given zeros:
-2, 2, 4
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Extra Practice
1. Find the real or imaginary solutions of the equation by factoring: 4x2=-4x-1
2. Find the real roots of the equation by graphing: x2+3=x3-5
