CAPITULO X
Descomposición Factorial
Descomposición Factorial
- Ejercicio 89
Factorar o descomponer en dos factores:
- a 2 +ab=a( a+b )
- b+ b 2 =b( 1+b )
- x 2 +x=x( x+1 )
- 3 a 3 – a 2 = a 2 ( 3a–1 )
- x 3 –4 x 4 = x 3 ( 1–4x )
- 5 m 2 +15 m 3 =5 m 2 ( 1+3m )
- ab+bc=b( a+c )
- x 2 y+ x 2 z= x 2 ( y+z )
- 2 a 2 x+6a x 2 =2ax( a+3x )
- 8 m 2 –12mn=4m( 2m–3n )
- 9 a 3 x 2 –18a x 3 =9a x 2 ( a–2x )
- 15 c 3 d 2 +60 c 2 d 3 =15 c 2 d 2 ( c+4d )
- 35 m 2 n 3 –70 m 3 =35 m 2 ( n 3 –2m )
- abc+ab c 2 =abc( 1+c )
- 24 a 2 x y 2 –36 x 2 y 4 =12x y 2 ( 2 a 2 –3x y 2 )
- a 3 + a 2 +a=a( a 2 +a+1 )
- 4 x 2 –8x+2=2( 2 x 2 –4x+1 )
- 15 y 3 +20 y 2 –5y=5y( 3 y 2 +4y–1 )
- a 3 – a 2 x+a x 2 =a( a 2 –ax+ x 2 )
- 2 a 2 x+2a x 2 –3ax=ax( 2a+2x–3 )
- x 3 + x 5 – x 7 = x 3 ( 1+ x 2 – x 4 )
- 14 x 2 y 2 –28 x 3 +56 x 4 =14 x 2 ( y 2 –2x+4 x 2 )
- 34a x 2 +51 a 2 y–68a y 2 =17a( 2 x 2 +3ay–4 y 2 )
- 96–48m n 2 +144 n 3 =48( 2–m n 2 +3 n 3 )
- a 2 b 2 c 2 – a 2 c 2 x 2 + a 2 c 2 y 2 = a 2 c 2 ( b 2 – x 2 + y 2 )
- 55 m 2 n 3 x+110 m 2 n 3 x 2 –220 m 2 y 3 =55 m 2 ( n 3 x+2 n 3 x 2 –4 y 3 )
- 93 a 3 x 2 y–62 a 2 x 3 y 2 –124 a 2 x=31 a 2 x( 3axy–2 x 2 y 2 –4 )
- x– x 2 + x 3 – x 4 =x( 1–x+ x 2 – x 3 )
- a 6 –3 a 4 +8 a 3 –4 a 2 = a 2 ( a 4 –3 a 2 +8a–4 )
- 25 x 7 –10 x 5 +15 x 3 –5 x 2 =5 x 2 ( 5 x 5 –2 x 3 +3x–1 )
- x 15 – x 12 +2 x 9 –3 x 6 = x 6 ( x 9 – x 6 +2 x 3 –3 )
- 9 a 2 –12ab+15 a 3 b 2 –24a b 3 =3a( 3a–4b+5 a 2 b 2 –8 b 3 )
- 16 x 3 y 2 –8 x 2 y–24 x 4 y 2 –40 x 2 y 3 =8 x 2 y( 2xy–1–3 x 2 y–5y )
- 12 m 2 n+24 m 3 n 2 –36 m 4 n 3 +48 m 5 n 4 =12 m 2 n( 1+2mn–3 m 2 n 2 +4 m 3 n 3 )
- 100 a 2 b 3 c–150a b 2 c 2 +50a b 3 c 3 –200ab c 2 =50abc( 2a b 2 –3b c 2 + b 2 c 2 –4 c 2 )
- x 5 – x 4 + x 3 – x 2 +x=x( x 4 – x 3 + x 2 –x+1 )
- a 2 –2 a 3 +3 a 4 –4 a 5 +6 a 6 = a 2 ( 1–2a+3 a 2 –4 a 3 +6 a 4 )
- 3 a 2 b+6ab–5 a 3 b 2 +8 a 2 bx+4a b 2 m=ab( 3a+6–5 a 2 b+8ax+4bm )
- a 20 – a 16 + a 12 – a 8 + a 4 – a 2 = a 2 ( a 18 – a 14 + a 10 – a 6 + a 2 –1 )