Б) ax² + bx + c = a(x - x₁)(x - x₂)
(4a² - 20a + 25) / (2a-5)
4a² - 20 a + 25 = 0
D = 400 -4*25*4 = 0
x₁ = (20 + 0) / 2*4 = 2.5
x₂ = (20 - 0) / 2*4 = 2.5
4a₂ - 20a + 25 = 4(x - 2.5)(x - 2.5) = 2(x - 2.5) * 2(x - 2.5) = (2x-5)(2x-5)
(2x-5)(2x-5) / (2x-5) = 2x-5
ч.т.д.
Г) (4a² - 11a - 3) / (a - 3)
4a² -11a - 3 = 0
D= 121 -4*4*(-3) = 169 = 13²
a₁ = (11 + 13) / 2*4 = 3
a₂ = (11 - 13) / 2*4 = -0.25
4a² -11a +3 = 4(a + 0.25)(a - 3) = (a-3)(4a+1)
(a-3)(4a+1) / (a-3) = 4a + 1
ч.т.д.