Question

Разложите многочлен на множители 4) x^3-8+(x+2)^2-2x 5) x^3-27+(x+3)^2-3x 6) 1+x^3+(x-1)^2+x

Answer 1

4) (x³ - 2³) + ( x + 2)² - 2x = (x - 2)(x²+2x+4) + (x² + 4x + 4 - 2x) =
= ( x- 2)(x² + 2x + 4) + (x² + 2x + 4) = ( x² + 2x + 4)(x- 2 + 1)=(x²+2x+4)(x - 1)

5) (x³ - 3³) + (x²+ 6x + 9 - 3x)= (x - 3)(x² +3x+9) +(x² + 3x + 9) =(x²+3x+9)(x- 3 + 1)=
= (x² + 3x + 9)(x - 2)

6) (1³ + x³) + (x²-2x + 1 + x) = (1 + x)(1 - x + x²) + (x² - x + 1) = (x² - x+1)(1 + x + 1)=
( x² - x + 1)(x + 2)