Question

Descompuneti in factori:
a) $3 x^{10}+9 x^{8}$
b)$x(x+1)-x-1$
c)$x^{2}(x+1)+x(x-1)^{2}$

Answer 1

a).  ... = 3x⁸ (x²+3) ;
b).  x (x+1 - (x+1) = (x+1) (x-1) ;
c).x [x(x+1)+(x-1)²] = x (x²+x+x²-2x+1) = x (2x²-x+1) ;

Answer 2

a) 3x¹⁰ + 9x⁸ = 3x⁸( x² + 3)
b) x( x + 1) - x - 1 = x( x+ 1 ) - 1( x + 1) = ( x + 1)(x - 1) = x² - 1
c) x²( x + 1) + x( x + 1)² = ( x + 1)[ x² + x( x + 1)] = ( x+ 1)(x² + x² + x) =
                                   = (( x+ 1)( 2x² + x) = x( x + 1)( 2x + 1)