The polynomial of degree $$ 5, P(x) $$, has leading coefficient 1 , has roots of multiplicity 2 at $$ x=1 $$ and $$ x=0 $$, and a root of multiplicity 1 at $$ x=-5 $$. Find a possible formula for $$ P(x) $$. $$ P(x)=x^{5}+3 x^{4}-9 x^{3}+5 x^{2} $$

Question

Mitchell Lang · Accepted Answer

A possible formula for $$ P(x) $$ is $$ P(x) = x^{5}+3x^{4}-9x^{3}+5x^{2} $$.

The polynomial of degree \( 5, P(x) \), has leading coefficient 1 , has roots of multiplicity 2 at \( x=1 \) and \( x=0 \), and a root of multiplicity 1 at \( x=-5 \). Find a possible formula for \( P(x) \). \( P(x)=x^{5}+3 x^{4}-9 x^{3}+5 x^{2} \)

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The polynomial of degree \( 5, P(x) \), has leading coefficient 1 , has roots of multiplicity 2 at \( x=1 \) and \( x=0 \), and a root of multiplicity 1 at \( x=-5 \). Find a possible formula for \( P(x) \). \( P(x)=x^{5}+3 x^{4}-9 x^{3}+5 x^{2} \)

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