POLINOMIOS

Alumno/a

R-04-03

Fecha

OPERACIONES CON POLINOMIOS. SUMA Y RESTA 1. Encuentra expresiones algebraicas equivalentes a las siguientes, para ello realiza las operaciones que sean necesarias. a) 2 · (a + b) + 3a – 5b = x

b) 2 ·   1  2 x  2  c) 3 · [2 · (5x – 3) + 4] – 10x =

d) – [– (x + 1)] = e) 2a · (b + a) – 3a2 = f) 5x · (y + z) – (4yx – 2xz) =

g)

1 a  ·  6b    a  2b   3  3 

h) x · (2 – x) + x2 =

2. Dados los polinomios P (x) = 4x5 – 3x2 + 2x + 2; Q (x) = 5x4 – 3x3 + x2 – x – 1 y R (x) = 3x5 – 2x3 + 5, calcula: a) P (x) + Q (x) – R (x)

c) 2 · P (x) – 3 · Q (x)

b) Q (x) – 2 · R (x)

d) 3 · P (x) – 2 · Q (x) + R (x)

04

POLINOMIOS Alumno/a

R-04-03 04

Fecha

3. Realiza las siguientes operaciones: a) (3x2 + 5x + 1) · (2x2)

d) (– x4 – 3x2 + 1) · (x3 – 2)

b) (4x3 – 2x + 2) · (2x + 1)

e) (4x2 – 6x + 1) : (2x + 1)

c) (x5 – 4x3 + 2x) · (x2 – 1)

f) (x5 + 2x4 – 5x3 – x2 – 14x – 15) : (x2 + 2)

4. Efectúa las siguientes operaciones: a) [(2x2 – 3x + 1) – (4x2 + x – 3)] · (2x + 3)

c) [(x4 – x2 + x) – (x5 + x4 – x2)] · (2x + 1)

b) (2x3 + 3x – 1) · (x2 + x) · x

d) [(x6 + 2x5 + x3) + (x4 + x6 – 4x3)] · 2x3

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