Why some polynomial zeros repeat and how they shape a graph
In short: In algebra, a polynomial's degree does not always equal its number of distinct zeros. This video explains the concept of multiplicity and how it dictates the way a polynomial behaves near its intercepts.
The video explores how factors within a polynomial determine its zeros and their multiplicity. For example, in the 3rd degree polynomial p(x)=(x-1)(x-3)², the zero x=3 has a multiplicity of 2 because the factor (x-3) repeats twice, while x=1 has a multiplicity of 1.
Understanding multiplicity is essential because it is directly related to the graphical behavior of the polynomial around each zero.
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Sources
- Summary by Intellect · source: Multiplicity of zeros of polynomials | Polynomial graphs | Algebra 2 | Khan Academy
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