What counts as a polynomial (integral rational) equation
If, after moving all terms to one side, you obtain a polynomial equation P(x)=0P(x)=0, it is called a polynomial (integral rational) equation. In grade 9 two typical cases matter: 1) biquadratic ax4+bx2+c=0ax^4+bx^2+c=0 (substitution t=x2t=x^2), 2) equations solved by factoring and the rule uv=0⇒u=0 or v=0uv=0\Rightarrow u=0\ \text{or}\ v=0.
Always check: after t=x2t=x^2, values of tt must be nonnegative before you return to xx
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