Interpret terms, factors, and coefficients in polynomial and rational expressions.
Interpret a repeated factor by zero, multiplicity, parity, and context
Problem
Interpret the repeated factor \((x~-~2)^2\). State its zero, multiplicity and parity, graph behavior, and meaning.
Big Picture
What this problem is really about
Separate the base factor from its exponent. Solving the base factor gives one zero, while the exponent tells how many times that same zero is repeated; it does not create several distinct zeros. Then use parity: odd multiplicity changes sign and crosses the axis, whereas even multiplicity keeps the same sign and touches before turning.
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