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## Sagot :

1.

**The function is of degree 10:**

- The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] in the polynomial.

- In [tex]\( y = x^4 + 4x^3 + 5x^2 + 4x + 4 \)[/tex], the highest power of [tex]\( x \)[/tex] is 4.

- Therefore, the degree of this polynomial is 4, not 10.

- This statement is

**false**.

2.

**The function has at least one zero in the set of complex numbers:**

- According to the Fundamental Theorem of Algebra, every non-constant polynomial has at least one complex root.

- Since our polynomial is of degree 4 (which is non-constant), it must have at least one complex root.

- This statement is

**true**.

3.

**The function has a zero with a multiplicity of 5:**

- The multiplicity of a zero is the number of times that zero appears as a root of the polynomial.

- Since the polynomial is of degree 4, the maximum possible multiplicity for any zero would be 4.

- Therefore, it is impossible for this polynomial to have a zero with a multiplicity of 5.

- This statement is

**false**.

4.

**The function cannot be graphed:**

- A polynomial function can always be graphed because it is a continuous and smooth function.

- Therefore, this statement is

**false**.

In summary, the only true statement about the polynomial [tex]\( y = x^4 + 4x^3 + 5x^2 + 4x + 4 \)[/tex] is:

**The function has at least one zero in the set of complex numbers.**