The polynomial of degree 4, $P(x)$, has a root of multiplicity 2 at $x=1$ and roots of multiplicity 1 at $x=0$ and $x=-4$. It goes through the point $(5,504)$. Find a formula for $P(x)$.
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The sum of the multiplicities must equal the degree of the polynomial, i.e., $m_1 + m_2 + \dots + m_k = n$. Given: Degree of the polynomial is 4. Root at $x=1$ with multiplicity 2. This means $(x-1)^2$ is a factor. Root at $x=0$ with multiplicity 1. This means Show more…
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