Question

3.9 factorización de polinomios pasando cambio de variable parte 2



factoriza:


a)4x²-(y+2)²


b)y²-2(x+3)y+(x+3)²​

Answer 1

Diferentes formas cualquiera esta bien:

Geometric figure:

hyperbolic paraboloid

Alternate forms:

(a^2 x - y - 2) (a^2 x + y + 2)

a^4 x^2 + (-y - 4) y - 4

Expanded form:

a^4 x^2 - y^2 - 4 y - 4

Roots:

y = a^2 (-x) - 2

y = a^2 x - 2

Polynomial discriminant:

Δ_x = 4 a^4 (y^2 + 4 y + 4)

Properties as a function:

Domain

R^2

Range

{z element R : a!=0 or z<=0}

Derivative:

d/dx(a^4 x^2 - (y + 2)^2) = 2 a^4 x

Indefinite integral:

integral(a^4 x^2 - (2 + y)^2) dx = (a^4 x^3)/3 - x (y + 2)^2 + constant