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Hi again bobbym!
are equal to
So you have this equation to solve
solving for r3 you get r3 = -1 which is the third root.
Well, as you know that cubic = linear x quadratic you can sort of figure out the quadratic coefficients as you go. It takes less time but amounts to short cut division so it's not really a new method.
So, Is division the only way?
hi Agnishom and Au101
you might notice that
which means you know (x+1) is factor straight away by the factor theorem.
In general, dividing by known factors is the way.
ps. For typical exam questions, they cannot choose factors that would take a long time to find, so I always do a quick mental check for x = +/-1, +/-2, +/-3. If I haven't found a factor by then I do another quicker question first.
I'm not sure what exactly your approach would be. Originally, I just posted my approach:
(By polynomial long-division)
Therefore, the other zero is -1
But having re-read your first post, I think that might be what you would have done anyway. I'm not sure that I know any more efficient method. But I suggest you just divide once and then factorise, that - at least - might make things a little faster?
The two zeros of a polynomial areand
and the polynomial is
What is the third zero?
My approach to such kinds of problem is to divide the polynomial by the two given factors to obtain the other factor and then the zero.
Can Someone suggest a quicker and more efficient method?