Question

Sa se descompuna in factori
a)[tex] x^{2} +15x+54
[/tex]
b)[tex] 6x^{2}+x-2
[/tex]

Answer 1

a) x²+15x+54 = 0.

a = 1
b = 15
c = 54

∆ = b²-4ac
∆ = 15²-4•54
∆ = 225-216
∆ = 9.

x1 = -b+√∆/2a
x1 = -15+3/2
x1 = -12/2
x1 = -6.

x2 = -b-√∆/2a
x2 = -15-3/2
x2 = -18/2
x2 = -9.

a(x-x1)(x-x2) = (x+6)(x+9).


b) 6x²+x-2 = 0.

a = 6
b = 1
c = -2

∆ = b²-4ac
∆ = 1-4•(-2)•6
∆ = 1+48
∆ = 49.


x1 = -b+√∆/2a
x1 = -1+7/12
x1 = 6/12
x1 = 1/2.

x2 = -b-√∆/2a
x2 = -1-7/12
x2 = -8/12
x2 = -2/3.


a(x-x1)(x-x2) = 6(x-1/2)(x+2/3) = 6(2x/2-1/2)(3x/3+2/3) = (2x-1)(3x+2).



Succes!

Answer 2

a) x²+15x+54=x²+9x+6x+54=
x(x+9)+6(x+9)=(x+9)(x+6)

b)6x²+x-2=6x²-3x+4x-2=3x(2x-1)+2(2x-1)=(2x-1)(3x+1)