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px³+3x²-3 and 2x³-5x+p leave the same remainder when divided by x-4.
According to the Remainder theorem,
When f(x) is divided by x-a, the remainder is f(a).
So, putting in 4 in both equations,
p×4³ + 3×4² - 3 = 2×4³ - 5×4 + p
64p + 48 - 3 = 128 - 20 + p
63p = 63
p = 1