10. Determine if g(x) divides f(x) in the given rings of polynomials (show your work): a) g(x) x55x4 + 15x³ 25x² + 17x 24 in Q[x]. = x² 3x + 8 and f(x) = b) g(x) = x² + x + 2 and f(x) = 3x5 + 3x¹ + 6x in Z7[x]

3.2 (2) Divides the polynomial

Consider the polynomial p(x) = 2 (x + 1) (x – 3)² (A) As х — —с0 y →? (В) As y →? (C) Find the zeros and their multiplicities.

b) The polynomial, fW) =2x" +mz -3, where m and n are real constants, is divisible by (x+1) but leaves a femiAder remainder of 156 when divided by (X-3). Find the valves of n and m.