1. **State the problem:** Multiply the polynomials $ (x + 2)(x^3 - 6x + 3) $. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in the first polynomial by each term in the second polynomial. 3. **Multiply each term:** - Multiply $x$ by each term in $x^3 - 6x + 3$: $$x \cdot x^3 = x^4$$ $$x \cdot (-6x) = -6x^2$$ $$x \cdot 3 = 3x$$ - Multiply $2$ by each term in $x^3 - 6x + 3$: $$2 \cdot x^3 = 2x^3$$ $$2 \cdot (-6x) = -12x$$ $$2 \cdot 3 = 6$$ 4. **Write all terms together:** $$x^4 - 6x^2 + 3x + 2x^3 - 12x + 6$$ 5. **Combine like terms:** - The $x^4$ term stands alone. - Combine $2x^3$ (only one cubic term). - Combine $-6x^2$ (only one quadratic term). - Combine $3x$ and $-12x$: $$3x - 12x = -9x$$ - Constant term is $6$. 6. **Final expression:** $$x^4 + 2x^3 - 6x^2 - 9x + 6$$ **Answer:** $$(x + 2)(x^3 - 6x + 3) = x^4 + 2x^3 - 6x^2 - 9x + 6$$