Answer :
We begin with the two polynomials:
$$5x^3 + 7x - 8 \quad \text{and} \quad 2x^3 - 5x^2 - x + 3.$$
**Step 1. Arrange and identify like terms**
Write both polynomials with all terms (note that the first polynomial has no $x^2$ term):
- First polynomial: $$5x^3 + 0x^2 + 7x - 8.$$
- Second polynomial: $$2x^3 - 5x^2 - x + 3.$$
**Step 2. Combine like terms**
1. **$x^3$ terms:**
$$5x^3 + 2x^3 = 7x^3.$$
2. **$x^2$ terms:**
$$0x^2 - 5x^2 = -5x^2.$$
3. **$x$ terms:**
$$7x - x = 6x.$$
4. **Constant terms:**
$$-8 + 3 = -5.$$
**Step 3. Write the simplified expression**
After combining like terms, the simplified expression in standard form is:
$$7x^3 - 5x^2 + 6x - 5.$$
This corresponds to option B.
$$5x^3 + 7x - 8 \quad \text{and} \quad 2x^3 - 5x^2 - x + 3.$$
**Step 1. Arrange and identify like terms**
Write both polynomials with all terms (note that the first polynomial has no $x^2$ term):
- First polynomial: $$5x^3 + 0x^2 + 7x - 8.$$
- Second polynomial: $$2x^3 - 5x^2 - x + 3.$$
**Step 2. Combine like terms**
1. **$x^3$ terms:**
$$5x^3 + 2x^3 = 7x^3.$$
2. **$x^2$ terms:**
$$0x^2 - 5x^2 = -5x^2.$$
3. **$x$ terms:**
$$7x - x = 6x.$$
4. **Constant terms:**
$$-8 + 3 = -5.$$
**Step 3. Write the simplified expression**
After combining like terms, the simplified expression in standard form is:
$$7x^3 - 5x^2 + 6x - 5.$$
This corresponds to option B.
