Is it a 5th degree Polynomial?

Algebra Level 4

a+4b+9c+16d+25e=14a+9b+16c+25d+36e=89a+16b+25c+36d+49e=23\large \begin{aligned} a + 4b + 9c + 16d + 25e & = 1 \\ 4a + 9b + 16c + 25d + 36e & = 8 \\ 9a + 16b + 25c+ 36d + 49e & = 23 \end{aligned}

Real numbers aa, bb, cc, dd, and ee satisfy the system of equations above. Find a+b+c+d+ea + b + c+ d + e.

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