Question

Descompuneți în factori:
a)x^2+5x+4
b)x^2+7x+6
c)x^2+9x+8
d)x^2-5x+4
e)x^2-8x+7

Ajutoooooor! Am nevoie urgent!

Answer 1

a)x^2+5x+4 = x^2 + x + 4x + 4 = x(x + 1) + 4(x + 1) =(x + 1)(x + 4)

b)x^2+7x+6 = x^2 + x + 6x + 6 = x(x + 1) + 6(x + 1) = (x + 1)(x + 6)

c)x^2+9x+8 = x^2 + x + 8x + 8 = x(x + 1) + 8(x + 1) = (x + 1)(x + 8)

d)x^2-5x+4 = x^2 - x - 4x + 4 = x(x - 1) - 4(x - 1) = (x - 1)(x - 4)

e)x^2-8x+7 = x^2 - x - 7x + 7 = x(x - 1) - 7(x - 1) = (x - 1)(x - 7) 

Answer 2

a)x²+5x+4=
Δ=b²-4ac=25-16=9
x₁=(-b+√Δ)/2a=(-5+3)/2=-1
x₂=(-b-√Δ)/2a=(-5-3)/2=-4
a(x-x₁)(x-x₂)=(x-(-1)(x-(-4)=(x+1)(x+4)

b)x²+7x+6
Δ=b²-4ac=49-24=25
x₁=(-b+√Δ)/2a=(-7+5)/2=-1
x₂=(-b-√Δ)/2a=(-7-5)/2=-6
a(x-x₁)(x-x₂)= (x +1)(x+6)

 c)x²+9x+8
Δ=b²-4ac=81-32=49
x₁=(-b+√Δ)/2a=(-9+7)/2= - 1
x₂=(-b-√Δ)/2a=(-9-7)/2= - 8
a(x-x₁)(x-x₂)= (x + 1)(x + 8)

 d)x²-5x+4=0
Δ=b²-4ac=25-16=9
x₁=(-b+√Δ)/2a=(5+3)/2= 4
x₂=(-b-√Δ)/2a=(5-3)/2= 1
a(x-x₁)(x-x₂)= (x - 1)(x - 4)

 e)x²-8x+7

Δ=b²-4ac=64-28=36
x₁=(-b+√Δ)/2a=(8+6)/2= 7
x₂=(-b-√Δ)/2a=(8-6)/2=1
a(x-x₁)(x-x₂)= (x - 1)(x - 7)