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Polynomials and Factors

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?

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If the polynomial of degree 3 has two factors (x+5) and (2x-1), then they are infinite numbers of polynomial that ...

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Polynomials and factors are investigated.

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