Polinomios 25 05 25

Apuntes

**Polinomios 05 05 25** --- **Main Subtopics:** • Polynomials and their sums • Polynomial subtraction • Polynomial multiplication • Polynomial products with specific functions --- ### Polynomials and their sums **I) P(x) + T(x)** P(x) = 5x³ - 4x + 9 T(x) = 5x³ + x² - 4x + 7 Sum: = (5x³ + 5x³) + (0 + x²) + (-4x - 4x) + (9 + 7) = 10x³ + x² - 8x + 16 --- **II) R(x) + Q(x)** R(x) = x⁴ + 3x³ - 9 Q(x) = 4x² + 6x - 8 Sum: = x⁴ + 3x³ + 4x² + 6x - 9 - 8 = x⁴ + 3x³ + 4x² + 6x - 17 --- **III) S(x) + P(x)** S(x) = -3x² + y² - x (assuming y² is a constant or a typo, but keeping as is) P(x) = 5x³ - 4x + 9 Sum: = 5x³ - 3x² - x + y² + 9 **Note:** Since y² appears, it might be a constant term or a typo; keeping as is. --- **IV) Q(x) + R(x)** Q(x) = 4x² + 6x - 8 R(x) = x⁴ + 3x³ - 9 Sum: = x⁴ + 3x³ + 4x² + 6x - 8 - 9 = x⁴ + 3x³ + 4x² + 6x - 17 --- **V) R(x) + S(x)** R(x) = x⁴ + 3x³ - 9 S(x) = -3x² + y² - x Sum: = x⁴ + 3x³ - 3x² - x + y² - 9 --- ### Polynomial subtraction **I. P(x) - T(x)** P(x) = 5x³ - 4x + 9 T(x) = 5x³ + 3x + 4x + 2 (probably 4x + 2, but seems inconsistent; assuming T(x) = 5x³ + 3x + 4x + 2, which simpl...