Question

E(x)=(x² - 4x) ( x² - 4x +5)+6

Answer 1

$E(x) = ( {x}^{2} - 4x)( {x}^{2} - 4x + 5) + 6$

$= ( {x}^{4} - 4 {x}^{3} + 5 {x}^{2} - 4 {x}^{3} + 16 {x}^{2} - 20x) + 6$

$= {x}^{4} + 21 {x}^{2} - 20x + 6$

Answer 2

Notam x²-4 = a => a(a+5)+6 = a²+5a+6=a²+2a+3a+6=a(a+2)+3(a+2) = (a+2)(a+3)= (x²-4x+2)(x²-4x+3)= (x²-4x+2)(x²-x-3x+3)=(x²-4x+2)x(x-1)-3(x-1)=(x²-4x+2)(x-1)(x-3)