Final answer:
To write the given polynomials in standard form, you subtract the terms of the second polynomial from those of the first, resulting in the polynomial 6x³ + x² + 7x - 9.
Step-by-step explanation:
To write the polynomial in standard form, we begin by subtracting the second polynomial from the first: (9x³ - 8x² + 5x - 6) - (3x³ - 9x² - 2x + 3). We do this by subtracting each corresponding term in the second polynomial from the first:
- Subtract the cubic terms: 9x³ - 3x³ = 6x³
- Subtract the quadratic terms: -8x² - (-9x²) = -8x² + 9x² = x²
- Subtract the x terms: 5x - (-2x) = 5x + 2x = 7x
- Subtract the constant terms: -6 - 3 = -9
Combining these results, we get the polynomial in standard form: 6x³ + x² + 7x - 9