February 21st, 2016, 12:26 PM  #1 
Newbie Joined: Feb 2015 From: Brazil Posts: 13 Thanks: 0 Math Focus: Still figuring it out.  Polynomials
A professor of mine said that we cannot multiply a polynomial with a negative leading coefficient by minus one to yield a positive leading coefficient. Ex: x³+5x²9x+5, then I do (1)(x³+5x²9x+5) to have x³5x²+9x5. He said that it produces a new graph and therefore is not like the original one. But in a textbook I have been using they seem to do it all the time. Can someone explain it to me? 
February 21st, 2016, 12:36 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
Your professor is right that you get a different graph. Multiplying by 1 reflects the graph in the xaxis. Perhaps if you give an example of when the textbook does it, we'll be able to explain why it doesn't matter in that context. 
February 21st, 2016, 12:41 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,831 Thanks: 2160 
Perhaps he wanted to know whether you'd promptly offer a good reason why what he'd said was wrong.

February 21st, 2016, 12:55 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 
Multiplying a polynomial by 1 will not change the location of function zeros, but it does reflect the graph over the xaxis

February 21st, 2016, 01:05 PM  #5 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
A good tip to find out what is happening is to try some simple known values for x to see if multiplying the polynomial through by 1 makes any difference. So here goes put x = 0 Then P = +5 and (1) P = 5, where P is the polynomial expression To show that x = 0 is not a special case try x = 2 Then P = 1 and (1) P = 1 But what happens if x = 1? Well P = 0 so (1)P = 0 = P and they are the same. So in the case where we convert our polynomial expression into an equation equal to zero we are justified and can multiply through by any convenient number That is solving the equation x³+5x²9x+5 = 0 is the same as solving the equation x³5x²+9x5 = 0 
February 21st, 2016, 06:03 PM  #6  
Newbie Joined: Feb 2015 From: Brazil Posts: 13 Thanks: 0 Math Focus: Still figuring it out.  Quote:
 

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