Question

4) Considerando os polinômios A = 6x3 + 5x2 - 8x + 15, B = 2x3 - 6x2 - 9x +
10 e C= x3 + 7x2 + 9x + 20. Calcule:
a) A + B + C
b) A-B-C​

Answer 1

Sendo:

A = 6x³ + 5x² — 8x + 15

B = 2x³ — 6x² — 9x + 10

C = x³ + 7x² + 9x + 20

Então:

a) A + B + C

= (6x³ + 5x² — 8x + 15) + (2x³ — 6x² — 9x + 10) + (x³ + 7x² + 9x + 20)

= 6x³ + 5x² — 8x + 15 + 2x³ — 6x² — 9x + 10 + x³ + 7x² + 9x + 20

= 6x³ + 2x³ + x³ + 5x² — 6x² + 7x² — 8x — 9x + 9x + 15 + 10 + 20

= 9x³ + 6x² — 8x + 45

b) A — B — C

= (6x³ + 5x² — 8x + 15) — (2x³ — 6x² — 9x + 10) — (x³ + 7x² + 9x + 20)

= 6x³ + 5x² — 8x + 15 — 2x³ + 6x² + 9x — 10 — x³ — 7x² — 9x — 20

= 6x³ — 2x³ — x³ + 5x² + 6x² — 7x² — 8x + 9x — 9x + 15 — 10 — 20

= 3x³ + 4x² — 8x — 15

Espero ter ajudado!