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In general, if a function f has a zero of odd multiplicity, the graph of y = f (x) will cross the x -axis at that x value. If a function f has a zero of even multiplicity, the graph of y = f (x) will touch the x …

Given the graph of a polynomial and looking at its x-intercepts, we can determine the factors the polynomial must have. Additionally, we can determine whether those factors are raised to an …

Relate polynomials to their graphs, where the polynomials have zeros with multiplicity greater than 1.

Given the graph of a polynomial and looking at its x-intercepts, we can determine the factors the polynomial must have. Additionally, we can determine whether those factors are raised to an …

To determine the multiplicity of a zero, you need to look at the polynomial in factored form and the exponent on each factor. For example, in the article above, it uses:

Multiplicity is just the degree (exponent) of each factor, or the amount of times a factor appears. If the multiplicity is even, the graph will “bounce” off the x-axis where that factor is zero. And if …

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It means that x=3 is a zero of multiplicity 2, and x=1 is a zero of multiplicity 1. Multiplicity is a fascinating concept, and it is directly related to graphical behavior of the polynomial around the …

Multiplicity is just the degree (exponent) of each factor, or the amount of times a factor appears. If the multiplicity is even, the graph will “bounce” off the x-axis where that factor is zero. And if …