What is the remainder when f(x) = 4x^20 - 7x^10 + x - 2 is divided by x - 1? If there is no remainder enter 0.

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The Remainder Theorem says that f(r) is the same as the remainder when the polynomial is divided by x - r.  Thus, by the Remainder Theorem, the value of f(1) will equal the remainder when f(x) is divided by x - 1.f(1) = 4(1)^20 - 7(1)^10 + (1) - 2       = 4(1) -7(1) + 1 - 2       = 4 - 7 + 1 - 2       = -4Therefore, when dividing f(x) by x - 1, you will have a remainder of -4.  This means that x - 1 is not a factor of f(x).