ax2 + bx + c is the standard form for quadratic.
ax3 + bx2 + cx + d for cubic etc etc
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That already is a polynomial in standard form.
The standard form of a polynomial of degree n is anxn + an-1xn-1 + ... + a1x + a0 where the ai are constants.
Powers of their exponents
x3 - 2x2 - 25x + 50 = 0
x3 + 4x2 - 25x - 100 = 0