Question

phân tích đa thức thành nhân tử :

a) (x - y + 5) ² - 2 (x - y + 5) + 1

b) x ⁵ + x + 1

c) x ³ + x ² + 4

d) x ⁴ + 2x ² - 24

 

Answer 1

a) (x-y+5)²-2(x-y+5)+1

=(x-y+5)-2(x-y+5).1+1²

=(x-y+5+1)²

=(x-y+6)²

Answer 2

b) x⁵ + x +1 = x⁵ + x + 1 + x² - x²

=( x⁵ - x²) + (x² + x +1)

=x²(x³ - 1) + (x² +x +1)

=x²(x - 1)(x² + x +1) + (x² + x +1)

=(x² + x +1)(x³ - x² +1)

Answer 3

c) x³ + x² +4 = x³ + 2x² - x² - 2x+ 2x +4

=x²(x+2) - x(x + 2) + 2(x + 2)

=(x+2)(x² - x +2 )

Answer 4

d) x⁴ + 2x² - 24 = (x²)² + 2.x².1 +1² - 25

=(x² + 1)² - 5²

=(x² + 1 +5)(x² +1 - 5)

=(x² + 6)(x² - 4)

=(x² +6 )(x-2)(x+2)