Adding Subtracting Polynomials 5E0Eb0

1. **State the problem:** We need to add the two polynomials $$2x^3 + x^2 - 3$$ and $$2x^2 + 4x - 1$$. 2. **Recall the rule:** When adding polynomials, combine like terms. Like terms have the same variable raised to the same power. 3. **Write the polynomials aligned by degree:** $$\begin{aligned} &2x^3 + x^2 + 0x - 3 \\ +&0x^3 + 2x^2 + 4x - 1 \end{aligned}$$ 4. **Add the coefficients of like terms:** - For $x^3$: $2 + 0 = 2$ - For $x^2$: $1 + 2 = 3$ - For $x$: $0 + 4 = 4$ - For constants: $-3 + (-1) = -4$ 5. **Write the resulting polynomial:** $$2x^3 + 3x^2 + 4x - 4$$ 6. **Check the options:** The correct answer is option b.) $2x^3 + 3x^2 + 4x - 4$. **Final answer:** $2x^3 + 3x^2 + 4x - 4$