Polinomios

Exemplos de polinômios

a) (3x²- 6x + 4) + (2x² + 4x – 7)= =3x²-6x+4+2x²+4x-7=
=3x²+2x²-6x+4x+4-7=
=5x²-2x-3

b)(5x²-4x+9)-(8x²-6x+3)=
=5x²-4x+9-8x²+6x-3=
=5x²-8x²-4x+6x+9-3=
=-3x²+2x+6

c) 4x(2x-3y ) =
=4x. 2x – 4x.3y
=8x² - 12xy

d) (3x + 5) . (x + 2)
= 3x(x+2) + 5(x + 2)=
=3x²+6x+5x+10
= 3x² + 11x + 10

e) p(x) = x³ + ax² + (b – 18)x + 1

p(1) = 0
1³ + a * 1² + (b – 18) * 1 + 1 = 0
1 + a + b – 18 + 1 = 0 a + b = 16

p(2) = 25
2³ + a * 2² + (b – 18) * 2 + 1 = 25
8 + 4a + 2b – 36 + 1 = 25
4a + 2b = 25 + 36 – 8 – 1
4a + 2b = 52 :(2)
2a + b = 26 a + b = 16
2a + b = 26 a = 16 – b
2 * (16 – b) + b = 26
32 – 2b + b = 26
– b = 26 – 32
– b = – 6 b = 6 a = 16 – b a = 16 – 6 a = 10

f) p(x) = 2x³ – kx² + 3x – 2k p(2) = 4
2 * 2³ – k * 2² + 3 * 2 – 2k = 4
16 – 4k + 6 – 2k = 4
– 4k – 2k = – 16 – 6 + 4
– 6k = –18 *(–1)
6k = 18 k = 3

g) (–2x² + 5x – 2) + (–3x³ + 2x – 1)

–2x² + 5x – 2 – 3x³ + 2x – 1

–2x² + 7x – 3x³ – 3

–3x³ – 2x² + 7x – 3

h) (–2x² + 5x – 2) – (–3x³ + 2x – 1)

–2x² + 5x – 2 + 3x³ – 2x + 1

–2x² + 3x – 1 + 3x³

3x³ – 2x² + 3x – 1

i)x – 1) * (x2 + 2x - 6)

x2 * (x – 1) + 2x * (x – 1) – 6 * (x – 1)

(x³ – x²) + (2x² – 2x) – (6x – 6)

x³ – x² + 2x² – 2x – 6x + 6

x³ + x² – 8x + 6

J) 4x2 – 10x – 5 e 6x + 12
(4x2 – 10x – 5) + (6x + 12)
4x2 – 10x – 5 + 6x + 12
4x2 – 10x + 6x – 5 + 12

4x2 – 4x + 7

(4x2 – 10x – 5) + (6x + 12) = 4x2 – 4x + 7

l) x2 – 3x – 1 com –3x2 + 8x – 6.

(x2 – 3x – 1) + (–3x2 + 8x – 6) → eliminar o segundo parênteses através do jogo de sinal.

+(–3x2) = –3x2
+(+8x) = +8x
+(–6) = –6

x2 – 3x – 1 –3x2 + 8x – 6 → reduzir os termos semelhantes.

x2 – 3x2 – 3x + 8x – 1 – 6

–2x2 + 5x – 7

Portanto: (x2 – 3x – 1) + (–3x2 + 8x – 6) = –2x2 + 5x –