Lecția 21. DESCOMPUNEREA ÎN FACTORI – pregătirea Evaluării Naționale 2020
• Noțiuni de reamintit
1. FACTOR COMUN
a) coeficientul :
2x±2y=2x±y
b) c.m.m.d.c. al coeficienților:
15x±20y=53x±4y
c) o literă:
3ab±5ac=a3b±5c
d) un grup de litere ( fiecare la puterea cea mai mică la care apare):
-1,7xy3z4±xyz2=xyz2-1,7±z2
e) c.m.m.d.c.al numerelor și un grup de litere:
2a2b3±27a3b=9a2b5b2±3a
f) paranteze în care sunt expresii algebrice:
x-1x+3+2-3xx-1=x-1x+3+2-3x=x-1x+3+2-3x=x-1-2x+5
2. UTILIZAREA FORMULELOR DE CALCUL PRESCURTAT
a2±2ab+b2=a+b2a2-b2=a-ba+b
Exemple:
a)
x2+12x+36=x2+2·5·x+62=x+629×2-30x+25=3×2-2·3x·5+52=3x-5249x2y4-16=7xy22-42=7xy2+47xy2-48×2-3y2=8×2-3y2=22x+3y22x-3
b)
2x+12-22x+13x-2+3x+22=2x+1-3x+22=-x-12=-1x+12=x+12
3. GRUPAREA TERMENILOR
Exemple:
a)
ax+by+ay+bx=ax+bx+ay+by=ax+y+bx+y=x+ya+b
b)
x2+5x+6=x2+2x+3x+6=xx+2+3x+2=x+2x+3×2-4x+3=x2-x-3x+3=xx-1-3x-1=x-1x-3×2+2x-3=x2-x+3x-3=xx-1+3x-1=x-1x+3×2-x-6=x2-3x+2x-6=xx-3+2x-3=x-3x+2
4. METODE COMBINATE
x4+x2+1==x4+2×2+1-x2==x2+12-x2==x2-x+1×2+x+1
• Observații
1) Putem descompune în termeni în etape:
Exemple:
55ab-44abc=115ab-4abc=11ab5-4cx+1x-1+x+1x-3=x+1x-1+x-3=x+12x-4=2x+1x-2
2) În general, descompunerea în factori este mai dificilă decât calculele cu numere reale reprezentate prin litere, așa că, dacă avem de arătat o idenititate, mai simplu este să prelucrăm membrul în care este descompunerea.
De exemplu: Arătați că
x3+2×2-5x-6=x+1x-2x+3
Rezolvare:
x+1x-2x+3==x2-2x+x-2x+3==x2-x-2x+3==x3+3x-x2-3x-2x-6==x3+2×2-5x-6
• Riscuri (greșeli)
Să greșim la calcule.
KIDI- sfat: Verificăm, folosind metoda explicată la Observația 2).
Felicitări! Ai terminat cursul!
„A N T R E N A M E N T U L KIDI-10”
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3. Question
1 pointsCorrect
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4. Question
1 pointsCorrect
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1 points150x-120y+60z=Correct
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1 pointsFolosind formula pătratului a trei termeni, restrângerea expresiei este:Correct
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Examples of questions from "Lecția 21. DESCOMPUNEREA ÎN FACTORI – pregătirea Evaluării Naționale 2020"
- 150x-120y+60z=
- . Atunci a=