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2. If 2x^3 - 9x^2 + 13x + k is divisible by x - 2, then it is also divisible by x -1.

I don't understand why this statement is true

8. An unknown polynomial f(x) of degree 37 yields a remainder of 1 when divided by x - 1, a remainder of 3 when divided by x - 3, a remainder of 21 when divided by x - 5.

Find the remainder when f(x) is divided by (x-1)(x-3)(x-5)

9. If ax^3 + bx + c, with a not equal 0, c not equal 0, has a factor of the form x^2 + px + 1, show that a^2 - c^2 = ab

10. Given that the cubic equation x^3 - 3x^2 + ax + b = 0 has rational coefficients and has the root - 1 + sqrt(3)i, determine the values of a and b.

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# Challenging math questions involving polynomial functions

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