SOLUTION: Give an example of a polynomial with degree 3 such that when factored, it contains the two factors (x+5) and (2x-1), i.e., the polynomial looks like (x+5)(2x-1)(?). How many such p

Question 76000: Give an example of a polynomial with degree 3 such that when factored, it contains the two factors (x+5) and (2x-1), i.e., the polynomial looks like (x+5)(2x-1)(?). How many such polynomials you think there are? What if I add the constraint that the value of this polynomial is zero when the variable x is equal to 1, how many such polynomials can you find?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You can have an infinite number of possible factors for the missing factor. For instance, we can have

or
or
etc
So we can continue this forever.
If we have the condition of one zero being x=1 then our factor must be
since if we have a zero of x=a we have a factor:
So we would have only one possible polynomial

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