Question

rozłóż wielomiany na czynniki

Answer 1

a) = 2x(3x-1)
b) = x^{4}(5x^{2}-3)
c) = 2x^{2}(x^{4}+ 7x^{5} +2 )
d) = (3x-4)(x+2)
e) = (4x^{2}+2)(x+2)
f) = x^{5} - 2x^{3} - 8x^{2} + 16 = (x^{5} - 2x^{3}) + (-8x^{2} + 16) =
=  x^{3}(x^{2} - 2) - 8(x^{2} - 2) = (x^{3} - 8)(x^{2}-2)

g) 
Δ=bx^{2} - 4ac = 16 - 8 = 12
\sqrt{Δ}= \sqrt{12}

x_1 = \frac{-bx^{2}-\sqrt{Δ}}{2a} = \frac{16}-\sqrt{12}}{8}
x_2 = \frac{-bx^{2}+\sqrt{Δ}}{2a} =  \frac{16}+\sqrt{12}}{8}

= 4(\frac{16}+\sqrt{12}}{8} + 1)(\frac{16}-\sqrt{12}}{8} - 1)(4x^{2}-1)

h) = 6(x^{2}-4)+(x^{2}-4)(x^{2}+4)
i) = (x+3)^{3} (x-3)

Δ= 36-36=0
\sqrt{Δ}= 0
x_0=-3

j) = (x^{3} + 3x^{2}) + (-5x-15) = -x^{2}(-x-3) +5(-x-3) = (-x^{2} + 5)(-x-3)

k) = 3x^{2}(x+2)-9(x+2)= (3x^{2}-9)(x+2)
l) = x^{2}(2x-1) + 1(2x-1) = x^{2}(2x-1)x^{2}
m) = 2x^{2}(x+2)+18(x+2)= (2x^{2}+18)(x+2)
n) = ...
o) = ...
p) = ...
r) = 3(\frac{-5-\sqrt{85}}{6}-5)(\frac{-5+\sqrt{85}}{6}-5)+1

 

 

Nie jestem pwena podpunktu i), g) i r). n), o) i p) niestety nie wyliczyłam.