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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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
%28x%2B5%29%282x-1%29%28x%29
or
%28x%2B5%29%282x-1%29%28x%2B2%29 or
%28x%2B5%29%282x-1%29%28x%2B22%29 etc
So we can continue this forever.
If we have the condition of one zero being x=1 then our factor must be
x-1=0 since if we have a zero of x=a we have a factor: x-a=0
So we would have only one possible polynomial
%28x%2B5%29%282x-1%29%28x-1%29