Question

26)Sa se descompuna in factori

Answer 1

Răspuns:

Explicație pas cu pas:

Voi nota cu semnul ~ puterea , de ex x~2 = x la puterea a doua

a) x~3+2x~2+x+2=X~2(x+2) +x+2 =(x+2)*(x~2+1)

X~3=X~2*X

scoatem in factor elementul comun, prima oara x~2, apoi (x+2)

b) (x+3)~2-1=(X+3-1)*(x+3+1)=(x+2)*(x+4)

folosim formula x~2-1=(x-1)*(x+1)

c) x~3+2x~2-4x-8= X~2*(x+2) - 4*(x+2)= (x+2)*(x~2-4)

d) x~4-(2x-1)~2 = (X~2)~2 - (2x-1)~2 = (X~2-2x+1)*(X~2 + 2x+1) = (X-1)~2*(X+1)~2

folosim formula x~2-y~2=(x-y)*(x+y)

apoi folosim formulele:

(X-1)~2=X~2 -2x +1 si

(x+1)~2 = X~2 + 2x+1

e) 4x~2 - (x+1)2 = (2x)~2 - (x+1)~2 = [2x - (x+1)]* [2x +(x+1)] = (x-1)(3x+1)

f) 81 - (x+3)~2 = 9~2 - (x+3)~2 = [9-(x+3)]*(9+x+3) = (6-x)*(x+12)

g) x~3+2x~2+3x+6 = x~2(x+2)+3(x+2) = (x+2)*(X~2+3)

h) 4x~3-x~2-16x+4 = x~2(4x-1) - 4(4x-1) = (4x-1)*(x~2-4)

i) 5x~3+3x~2 - 20x-12 = x~2*(5x+3) -4(5x-3) = (5x-3)*(x~2-4)

j) 2x~3-3x~2 - 18x+27 = x~2(2x-3) -9(2x-3) = (2x-3)*(x~2-9)