A Nice Algebra Question | 2 Different Methods | Sweden Junior Math Olympiad

[@RobertHering-tq7bn]

Made a simple try to use polynom division two times and replacing x³+4x by the given value. This resulted in the following way to get to the solution. x^7+64x²+2 = (x^4-4x²+16)*(x³+4x) + 64x²-64x+2 = (x^4-4x²+16)*8 + 64x²-64x+2 = 8x^4-32x²+128 + 64x²-64x+2 = 8x^4+32x²-64x+130 8x^4+32x²-64x+130 = 8x*(x³+4x) - 64x+130 = 8x*8 -64x+130 = 64x - 64x + 130 = 130

[@yakupbuyankara5903]

130

[@Taco-777c]

1