Question

Proszę o rozwiazania przykladow z zalacznika.

Answer 1

1a]

x³+2x²=x²(x+2)

c]

6x³-12x²+18x=6x(x²-2x+1)

b]

3x⁴+2x²=x²(3x+2)

d]

4x⁵-2x⁴+6x²=2x²(2x³-x²+3)

2a]

(x²+2)(2x-3)+(x²+2)(x+1)=(x²+2)(2x-3+x+1)=(x²+2)(3x-2)

b]

(3x²+1)(x-1)-(3x²+1)(2x+5)=(3x²+1)(x-1-2x-5)=(3x²+1)(-x-6)

c]

(x+2)(x²+6)-(x+2)(1-2x²)=(x+2)(x²+6-1+2x²)=(x+2)(3x²+5)

d]

(x²+1)(x+3)-(x+3)(4-3x²)=(x+3)(x²+1-4+3x²)=(x+3)(4x²-3)

3a]

4x²-9=(2x+3)(2x-3)

b]

9x²-30x+25=9(x-⁵/₃)²=3(3x-5)²

Δ=b²-4ac=900-900=0

x₀=-b/2a=30/18=⁵/₃

c]

-25x²-20x-4=-25(x+⅖)²=-5(5x-2)²

Δ=400-400=0

x₀=20/-50=-⅖

d]

(x²-8x+16)-(4x²+4x+1)=x²-8x+16-4x²-4x-1=

-3x²-12x+15=-3(x-1)(x+5)

Δ=144+180=324

√Δ=18

x₁/x₂=[-b-/+ √Δ]/2a

x₁=[12-18]/-6=1

x₂=[12+18]/-6=-5