Question

Dados os polinomios p(x)=2x3+x2-3x+1 e q(x)=2x4-x3+3x2+4,calcule p(x).q(x) .

Answer 1

p(x)= 2x3+x2-3x+1
q(x)= 2x4-x3+3x2+4

(2x³ + x² - 3x + 1) × (2x⁴ - x³ + 3x² + 4) =

[(2x³ × 2x⁴) + (2x³ × (- x³)) + (2x³ × 3x²) + (2x³ × 4)] + [(x² × 2x⁴) + (x² × (- x³)) + (x² × 3x²) + (x² × 4)] + [((- 3x) × 2x⁴) + ((- 3x) × (- x³)) + ((- 3x) × 3x²) + ((- 3x) × 4)] +  [(1 × 2x⁴) + (1 × (- x³)) + (1 × 3x²) + (1 × 4)] =

(4x⁷ - 2x⁶ + 6x⁵ + 8x³) + (2x⁶ - x⁵ + 3x⁴ + 4x²) + (- 6x⁵ + 3x⁴ - 9x³ - 12x) + (2x⁴ - x³ + 3x² + 4) = 

4x⁷ - 2x⁶ + 2x⁶ + 6x⁵ - x⁵ - 6x⁵ + 3x⁴ + 3x⁴ + 2x⁴ + 8x³ - 9x³ - x³ + 4x² + 3x² - 12x + 4 =

4x⁷ - x⁵ + 8x⁴ - 2x³ + 7x² - 12x + 4


p(x).q(x) = 4x⁷ - x⁵ + 8x⁴ - 2x³ + 7x² - 12x + 4