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Zeros and multiplicity
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Learn it A factor (x − r)ⁿ gives a zero at x = r with multiplicity n. Odd multiplicity: the graph crosses the x-axis there. Even multiplicity: it touches and turns back. A polynomial of degree n has at most n real zeros.
Example: y = (x − 2)²(x + 1). Describe the zeros.
- x = 2, multiplicity 2: touches the axis.
- x = −1, multiplicity 1: crosses the axis.
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