Ejercicio 100

Ejercicio 100

1. 2 x 2 +3x–2 =2 x 2 +4x–x–2 . 4 1 | 4 =2x( x+2 ) –( x+2 ) =( x+2 ) ( 2x–1 )
2. 3 x 2 –5x–2 =3 x 3 –6x+x–2 . 6 1 | 6 =3x( x–2 ) +( x–2 ) =( x–2 ) ( 3x+1 )
3. 6 x 2 +7x+2 =6 x 2 +3x+4x+2 . 12 6 3 1 | 2 2 3 =3x( 2x+1 ) +2( 2x+1 ) =( 2x+1 ) ( 3x+2 )
4. 5 x 2 +13x–6 =5 x 2 +15x–2x–6 . 30 15 1 | 2 15 =5x( x+3 ) –2( x+3 ) =( x+3 ) ( 5x–2 )
5. 6 x 2 –6–5x=6 x 2 –5x–6 =6 x 2 –9x+4x–6 . 36 18 9 1 | 2 2 =3x( 2x–3 ) +2( 2x–3 ) =( 2x–3 ) ( 3x+2 )
6. 12 x 2 –x–6 =12 x 2 +8x–9x–6 . 72 36 18 9 1 | 2 2 2 9 =4x( 3x+2 ) –3( 3x+2 ) =( 3x+2 ) ( 4x–3 )
7. 4 a 2 +15a+9 =4 a 2 +12a+3a+9 . 36 18 9 3 1 | 2 2 3 3 =4a( a+3 ) +3( a+3 ) =( a+3 ) ( 4a+3 )
8. 3+11a+10 a 2 =3+6a+5a+10 a 2 . 30 15 5 1 | 2 3 5 =3( 1+2a ) +5a( 1+2a ) =( 1+2a ) ( 3+5a )
9. 12 m 2 –13m–35 =12 m 2 –28m+15m–35 . 420 210 105 35 7 1 | 2 2 3 5 7 =4m( 3m–7 ) +5m( 3m–7 ) =( 3m–7 ) ( 4m+5m )
10. 20 y 2 +y–1 =20 y 2 +5y–4y–1 . 20 10 5 1 | 2 2 5 =5y( 4y+1 ) –( 4y+1 ) =( 4y+1 ) ( 5y–1 )
11. 8 a 2 –14a–15 =8 a 2 +6a–20a–15 . 120 60 30 15 5 1 | 2 2 2 3 5 =2a( 4a+3 ) –5( 4a+3 ) =( 4a+3 ) ( 2a–1 )
12. 7 x 2 –44x–35 =7 x 2 –49x+5x–35 . 245 49 1 | 5 49 =7x( x–7 ) +5( x–7 ) =( x–7 ) ( 7x+5 )
13. 16m+15 m 2 –15=15 m 2 +16m–15 =15 m 2 +25m–9m–15 . 225 75 25 1 | 3 3 25 =5m( 3m+5 ) –3m( 3m+5 ) =( 3m+5 ) ( 5m–3m )
14. 2 a 2 +5a+2 =2 a 2 +4a+a+2 . 4 1 | 4 =2a( a+2 ) +( a+2 ) =( a+2 ) ( 2a+1 )
15. 12 x 2 –7x–12 =12 x 2 –16x+9x–12 . 144 72 36 18 9 1 | 2 2 2 2 9 =4x( 3x–4 ) +3( 3x–4 ) =( 3x–4 ) ( 4x+3 )
16. 9 a 2 +10a+1 =9 a 2 +9a+a+1 . 9 1 | 9 =9a( a+1 ) +( a+1 ) =( a+1 ) ( 9a+1 )
17. 20 n 2 –9n–20 =20 n 2 –25n+16n–20 . 400 200 100 50 25 1 | 2 2 2 2 25 =5n( 4n–5 ) +4( 4n–5 ) =( 4n–5 ) ( 5n+4 )
18. 21 x 2 +11x–2 =21 x 2 +14x–3x–2 . 42 21 7 1 | 2 3 7 =7x( 3x+2 ) –( 3x+2 ) =( 3x+2 ) ( 7x–1 )
19. m–6+15 m 2 =15 m 2 +m–6 =15 m 2 +10m–9m–6 . 90 45 15 5 1 | 2 3 3 5 =5m( 3m+2 ) –3( 3m+2 ) =( 3m+2 ) ( 5m–3 )
20. 15 a 2 –8a–12 =15 a 2 +10a–18a–12 . 180 90 45 15 5 1 | 2 2 3 3 5 =5a( 3a+2 ) +6a( 3a+2 ) =( 3a+2 ) ( 5a+6a )
21. 9 x 2 +37x+4 =9 x 2 +36x+x+4 . 36 1 | 36 =9x( x+4 ) +( x+4 ) =( x+4 ) ( 9x+1 )
22. 44n+20 n 2 –15 =20 n 2 +4n–15=20 n 2 +50n–6n–15 . 300 150 75 25 5 1 | 2 2 3 5 5 =10n( 2n+5 ) –3( 2n+5 ) =( 2n+5 ) ( 10n–3 )
23. 14 m 2 –31m–10= 14 m 2 +4m–35m–10 . 140 70 35 1 | 2 2 35 =2m( 7m+2 ) –5( 7m+2 ) =( 7m+2 ) ( 2m–5 )
24. 2 x 2 +29x+90 =2 x 2 +20x+9x+90 . 180 90 45 15 5 1 | 2 2 3 3 5 =2x( x+10 ) +9( x+10 ) =( x+10 ) ( 2x+9 )
25. 20 a 2 –7a–40 =20 a 2 +25a–32a–40 . 800 400 200 100 50 25 1 | 2 2 2 2 2 25 =5a( 4a+5 ) –8a( 4a+5 ) =( 4a+5 ) ( 5a–8a )
26. 4 n 2 +n–33 =4 n 2 +12n–11n–33 . 132 66 33 11 1 | 2 2 3 11 =4n( n+3 ) –11( n+3 ) =( n+3 ) ( 4n–11 )
27. 30 x 2 +13x–10 =30 x 2 +25x–12x–10 . 300 150 75 25 1 | 2 2 3 25 =5x( 6x+5 ) –2( 6x+5 ) =( 6x+5 ) ( 5x–2 )