1. The problem asks us to form a polynomial with given real zeros $-2$, $-1$, $2$, and $3$, and degree $4$. 2. The polynomial can be expressed as the product of factors corresponding to each zero: $$f(x) = (x - (-2))(x - (-1))(x - 2)(x - 3) = (x + 2)(x + 1)(x - 2)(x - 3)$$ 3. First, multiply the first two factors: $$(x + 2)(x + 1) = x^2 + x + 2x + 2 = x^2 + 3x + 2$$ 4. Next, multiply the last two factors: $$(x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6$$ 5. Now multiply the two quadratic expressions: $$ (x^2 + 3x + 2)(x^2 - 5x + 6) $$ 6. Multiply term by term: $$x^2 \cdot x^2 = x^4$$ $$x^2 \cdot (-5x) = -5x^3$$ $$x^2 \cdot 6 = 6x^2$$ $$3x \cdot x^2 = 3x^3$$ $$3x \cdot (-5x) = -15x^2$$ $$3x \cdot 6 = 18x$$ $$2 \cdot x^2 = 2x^2$$ $$2 \cdot (-5x) = -10x$$ $$2 \cdot 6 = 12$$ 7. Combine like terms: $$x^4 + (-5x^3 + 3x^3) + (6x^2 - 15x^2 + 2x^2) + (18x - 10x) + 12$$ $$= x^4 - 2x^3 - 7x^2 + 8x + 12$$ 8. The polynomial with the given zeros and degree 4 is: $$\boxed{f(x) = x^4 - 2x^3 - 7x^2 + 8x + 12}$$