Question

(x^2-4)(x^2+x+1)=(x^2-4)(2x+13)

Answer 1

(x^2-4)(x^2+x+1)=(x^2-4)(2x+13)

              (x² - 4)(x² + x+ 1) = (x² - 4)(2x + 13)
(x⁴ + x³ + x² - 4x² - 4x - 4)  = (2x³ + 13x² - 8x - 52)
(x⁴ + x³        - 3x² - 4x - 4)  = 2x³ + 13x² - 8x - 52

x⁴ + x³ - 3x² - 4x - 4 = 2x³ + 13x² - 8x - 52  ( igualar a ZERO)

x⁴ + x³ - 3x² - 4x - 4 - 2x³ - 13x² + 8x + 52 = 0 ( junta termos iguais)
x⁴ + x³ - 2x³ - 3x² - 13x² - 4x + 8x - 4 + 52 = 0
x⁴     - x³          - 16x²           + 4x     + 48 = 0

x⁴ - x³ - 16x² + 4x + 48 = 0
(x - 4)(x - 2)(x + 2)(x + 3) = 0

(x - 4) = 0
x - 4 = 0
x = + 4

(x - 2) = 0
x - 2 = 0
x = + 2

(x + 2) = 0
x + 2= 0
x = - 2

(x + 3) = 0
x + 3 = 0
x = - 3