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# Synthetic division And the Remainder theorem One factor of f(x)=4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem. A) x = 1, x = 2, or x = 4 B) x = –2, x = 1, or x = 2 C) x = 2, x = 4, or x = 16 D) x = –16, x = 2, or x = 16

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The remainder theorem says that if is a factor of a polynomial , then the remainder of the split is 0, so that there is a lesser degree of the polynomial as the quotient of:Using the fact that it is a factor, you can find a quadratic equation that is easy to factor more.Synthetic division yieldswhich can be more of a factor that asSo,The roots are below .