Biologia

Factorizar y calcular las raíces de los polinomios

1 x3 + x2 = x2 (x + 1) La raíces son: x = 0 y x = − 1
2 2x4 + 4x2 = 2x2 (x2 + 2) Raíz: x= 0
3 x2 – 4= (X + 2)· (X − 2) Las raíces son: x = − 2 y x = 2
4 x4 – 16= (x2 + 4) · (x2 − 4) = (X + 2) · (X − 2) · (x2 + 4) Las raíces son: x= −2 y x = 2
5 9 + 6x + x2 = (3+ X)2 {32 2.3.X X2}La raíz es: x = −3
6= (x+2). (x-3) Las raíces son x = 3 y x = −2 
7 x2 − 10x + 9= (x + 1) · (x − 1) · (x + 3) · (x − 3)

Factorizar los polinomios
1 9x4 − 4x2 = x2 ·(9x2 − 4) = x2 · (3x + 2) · (3x − 2)
2 x5 + 20x3 + 100x = x · (x4 + 20x2 + 100) = x · (x2 + 10)2
3 2x3 − 50x = 2x · (x2 − 25) =2x · (x + 5) · (x - 5)
4 2x5 − 32x = 2x · (x4 −16) = 2x · (x2 + 4) · (x2 − 4) =
2x · (x2 + 4) ·(x +2) · (x − 2)
5 2x2 + x − 28 = 2x2 + x − 28 = 0
2x2 + x − 28 = 2 (x + 4) · (x − 7/2)
6 25x2 − 1=  (5x +1) · (5x − 1)
736x6 − 49 = (6x3 + 7) · (6x3 − 7)
8 x2 − 2x + 1 = (x − 1)2
9 x2 − 6x + 9 = (x- 3)2
10 x2 − 20x + 100 = (x − 10)2
11 x2 + 10x +25 = (x + 5)2
12 x2 + 14x + 49 = (x + 7)213 x3 − 4x2 + 4x = x · (x2 − 4x +4) = x · (x − 2)2

14 3x3 − 27x = 3x · (x6 − 9) = 3x · (x3 + 3) · (x3 − 3)
15 x2 − 11x + 30 = 0
16 3x2 + 10x + 3 = 0
17 2x2 − x – 1= 2(x − 1) · (x + 1/2)

Resolver las ecuaciones de primer grado

1 = x= 6/2 x=3
2 = 2x-x = 6+3 x=9
3 = 4x-6 = 6+x
4x – x = 6+6
3x=12 x= 12/3x= 4
4 = (6,2) = 6 x-1-3 (x-3)= -6 x-1-3x+9= -6 x-3x= -6 -9 +1 -2x= -14 2x=14 x=14/2 x=7
5 = 6/4x + 12/4 = x + 19 3/2x + 3 =x + 19 3x+6=2x+38 3x-2x = 38 – 6 x= 32
6 = 4x-40= -12 +6x – 6x 4x-6x+6x = -12+40 4x= 28 x=7
7 = 2x+2 -3x +6 = x+6 2x-3x –x = 6 -2 -6 -2x= -2 x=1