If x² + bx -2 is factor of xcubed + (2b-1)x² - p, find two possible values of p.
Im not sure what method to use to solve this. do i divide them?
Hello DetanonBecause when one factor of a cubic is a quadratic, the other is linear; i.e. it is of the form for some values of and .It doesn't mean anything. You have taken it out of context. Read the whole thing. I am comparing coefficients. (Do you know what thay means?) First I am looking at the coefficient of . Later on, I look at the coefficients of and the constant. I have used a colon (':') each time to show which coefficient I am looking at.and what does mean?
No, not a method that is as sensible and straightforward as the one I have shown you.Is there a different method to do it?
Read it through again - it's really very simple.
Grandad
Hello Detanon
I really don't know what your problem is here. Multiply out the brackets from
and then note that the result has to be identically equal to
(Can you do that?)
In this way you get the equations for and that I have shown you. I repeat: if you understand the basic rules of algebra, then trust me, this is really very simple. (And certainly much easier than trying to do an algebraic long division.)
Grandad
If is a factor then it should be obvious, after a little thought, that the other factor has to be . This is the only way that you can get the term and the constant term of .
So . Expand this out. You require the coefficient of to be and the coeffcient of to be zero:
.... (1)
.... (2)
Solve equations (1) and (2) simultaneously for b and p.
You need to go back now and have a good hard think about all that's been said about this question.
For checking purposes:
Spoiler: