Answer to Question #97951 in Algebra for Alexandra Villa-Molina

Question

You have worked with polynomial expressions so far, but you have not yet worked with polynomial equations. We will now focus on polynomial equations that are of degree 3 or higher. The process for solving these polynomial equations is not all that different than the processes used for solving quadratic equations. Your goal in solving these types of problems is actually to simplify the polynomial equation to quadratic and/or linear parts. You will often do this by factoring. As a review, briefly explain the process to check that the solution you found is correct

Answer 1

For the polynomial equation of degree higher than 2, that is other than quadratic equation, we can solve these equations by using a factorization. First we need to factorize the polynomial equation into quadratic equation or the linear equation. And when we will be able to factorize the higher degree polynomial equation into a lower degree of quadratic and linear, then we can easily find the roots of those quadratic and linear part of those polynomial equation.

Now to check whether the solution we found by using this method is correct or not, there are few ways.

For example:

1) Considering that we did the factorization part correct, then we can check our solution by putting the solution or roots of the polynomial equation in this equation.

Suppose the equation is ax³+bx²+ cx + d=0 and suppose the solution we find by the method of factoring is p, q and r.

Then we can put the value p, q and r one by one in the above equation and check if it satisfies the given polynomial equation or not.

2) If we can draw the graph of those polynomial equation and suppose the graph cuts the X-axis at some places, then we can check it from the solution we obtained from the factoring method, i.e., they are the same values at which the graph of polynomial equation cuts the X- axis.