Question

Rozłóż wielomian na czynniki:

1. W(x)=x³-x²

2) W(x)= x^4+6x³-5x²

Answer 1

1.

W(x)=x³-x²

W(x)=x²(x-1)

 

2.

W(x)=x⁴+6x³-5x²

W(x)=x²(x²+6x-5)

 

Answer 2

1.
W(x) = x³ - x²
= x²(x - 1)

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2)
W(x)= x^4+6x³-5x²
= x²(x² + 6x - 5)

a = 1 b = 6 c = -5
Δ = b² - 4ac

Δ = 6² - 4 * 1 * 5
Δ = 36 - 20
Δ = 16
√Δ = 4

x₁ = -b - √Δ / 2a
x₁ = -6 - 4 / 2 x 1
x₁ = -10 / 2
x₁ = -5

x₂ = -b + √Δ / 2a
x₂ = -6 + 4 / 2
x₂ = -2/2
x₂ = -1

W(x) = x²(x + 5) (x + 1)

Answer 3

w(x)= x^2(x-1)

w(x)=x^2(x^2+6x-5)