Question

1. Factorizati expresiile factorizate
a) x la a 3 + x la a 2 - 25x - 25
b) a la a 5 - a la a 3 + a la a 2 - 1
c) 4(x + 2) la a 2
d) x la a 4 + 2x la a 2

Answer 1

a) $(x^3+x^2)-(25x+25)=x^2(x+1)-25(x+1)=(x+1)(x^2-25)= \\ =(x+1)(x-5)(x+5)$
b)$(a^5-a^3)+(a^2-1)=a^3(a^2-1)+(a^2-1)=(a^2-1)(a^3+1)$
c)

Answer 2

a) x³ + x² - 25x - 25 = (x³ + x²) - (25x + 25) = x² · (x + 1) - 25 · (x + 1) = (x + 1) · (x² - 25) = (x + 1) · (x² - 5²) = (x + 1) · (x - 5) · (x + 5)

b) a⁵ - a³ + a² - 1 = (a⁵ - a³) + (a² - 1) = a³ · (a² - 1) + (a² - 1) = (a² - 1) · (a³ + 1) = (a - 1) · (a + 1) · (a³ + 1) = (a - 1) · (a + 1) · (a + 1) · (a² + a + 1)

c) 4 (x + 2)² =  4 · (x² + 2 · 2 ·x + 2²) = 4 · (x² + 4x + 4) 

d) x⁴ + 2x² = x² · (x² + 2)