Question #45160

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Question #45160

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Answer 1 · 2017-02-13T13:59:47

See explanation.

Explanation:

To solve this task you need to use the folloing feature of polynomial:

If $a$ $a$ is a zero of polynomial with multiplicity $n$ $n$ , then the polynomial is divisible by ${(x - a)}^{n}$ $(x-a)^n$ and not divisible by ${(x - a)}^{n + 1}$ $(x-a)^(n+1)$

As stated above the polynomial would have to be divisible by ${(x - 3)}^{3}$ $(x-3)^3$ , and ${(x - 0)}^{2}$ $(x-0)^2$ . The only polynomial of degree $5$ $5$ fulfilling theses conditions is:

$P (x) = {(x - 3)}^{3} \cdot x^{2} = (x^{3} + 3 x^{2} + 3 x + 1) \cdot x^{2}$ $P(x)=(x-3)^3*x^2=(x^3+3x^2+3x+1)*x^2$
$= x^{5} + 3 x^{4} + 3 x^{3} + x^{2}$ $=x^5+3x^4+3x^3+x^2$

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Question #45160

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