Question

Phân tích đa thức thành nhân tử:

a) 4x^4+1

b) 4x^4 +y^4

c) x^4+ 324

d) (x+2)(x+3)(x+4)(x+5)-24

e)x^3-6x^2-x+30

Answer 1

e, x³ - 6x² - x + 30

= x³ + 2x² - 8x² - 16x +15x + 30

= ( x³ + 2x²) -(8x² + 16x)+(15x +30)

= x²(x+2) - 8x(x + 2) + 15(x + 2)

= (x + 2)(x² - 8x + 15)

= (x + 2)( x² - 5x - 3x +15)

= (x + 2)[(x² - 5x ) - (3x -15)

= (x + 2)[ x(x - 5) - 3(x - 5)]

= (x + 2)[ (x - 5)(x - 3)]

= (x + 2)(x - 5)(x - 3)

Answer 2

a) 4x⁴ + 1 = 4x⁴ + 4x² + 1 - 4x²

= ( 2x² + 1 )² - ( 2x )²

= ( 2x² - 2x + 1 ) . ( 2x² + 2x + 1 )

b) 4x⁴ + y⁴ = 4x⁴ + 4x²y² + y⁴ - 4x²y²

= ( 2x² + y² )² - ( 2xy )²

= ( 2x² - 2xy + y² ) . ( 2x² + 2xy + y² )