The polynomial of degree $$ 5, P(x) $$, has leading coefficient 1 , has roots of multiplicity 2 at $$ x=2 $$ and $$ x=0 $$, and a root of multiplicity 1 at $$ x=-2 $$. Find a possible formula for $$ P(x) $$. $$ P(x)=\square $$

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To find a possible formula for the polynomial $$ P(x) $$ of degree 5 with the given conditions, we can use the factored form of a polynomial.

Given:
- Leading coefficient is 1.
- Roots of multiplicity 2 at $$ x=2 $$ and $$ x=0 $$.
- Root of multiplicity 1 at $$ x=-2 $$.

The factored form of a polynomial with the given roots is:
$$ P(x) = (x-2)^2(x-0)^2(x+2) $$

Now, we can simplify this expression to find the possible formula for $$ P(x) $$.
Simplify the expression by following steps:
- step0: Calculate:
  $$\left(x-2\right)^{2}\left(x-0\right)^{2}\left(x+2\right)$$
- step1: Remove 0:
  $$\left(x-2\right)^{2}x^{2}\left(x+2\right)$$
- step2: Reorder the terms:
  $$x^{2}\left(x-2\right)^{2}\left(x+2\right)$$
- step3: Rewrite the expression:
  $$\left(x+2\right)\left(x-2\right)^{2}x^{2}$$
- step4: Multiply the expression:
  $$\left(x+2\right)\left(x^{2}-2x\right)^{2}$$
- step5: Rearrange the terms:
  $$\left(x^{2}-2x\right)^{2}\left(x+2\right)$$
- step6: Expand the expression:
  $$\left(x^{4}-4x^{3}+4x^{2}\right)\left(x+2\right)$$
- step7: Apply the distributive property:
  $$x^{4}\times x+x^{4}\times 2-4x^{3}\times x-4x^{3}\times 2+4x^{2}\times x+4x^{2}\times 2$$
- step8: Multiply the terms:
  $$x^{5}+2x^{4}-4x^{4}-8x^{3}+4x^{3}+8x^{2}$$
- step9: Subtract the terms:
  $$x^{5}-2x^{4}-4x^{3}+8x^{2}$$
The possible formula for the polynomial $$ P(x) $$ is:
$$ P(x) = x^{5} - 2x^{4} - 4x^{3} + 8x^{2} $$
$$ P(x) = x^{5} - 2x^{4} - 4x^{3} + 8x^{2} $$

The polynomial of degree , has leading coefficient 1 , has roots of multiplicity 2 at and
, and a root of multiplicity 1 at .
Find a possible formula for .

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The polynomial of degree , has leading coefficient 1 , has roots of multiplicity 2 at and , and a root of multiplicity 1 at . Find a possible formula for .