Question

Phân tích đa thức thành nhân tử  (x+2)(x+3)(x+4)(x+5)-24

Answer 1

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

= (x²+7x+10)(x²+7x+12)-24

đặt y=x²+7x+10

ta có biểu thức:

y.(y+2)-24

= y²+2y-24

= y²+6y-4y-24

= y(y+6)-4(y+6)

= (y+6)(y-4)

= (x²+7x+10+6)(x²+7x+10-4)

= (x²+7x+16)(x²+7x+6)

Answer 2

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

= (x² + 3x + 2x + 6)(x² + 5x + 4x + 20) - 24

= (x² + 5x + 6)(x² + 9x + 20) - 24

= x⁴ + 9x³ + 20x² + 5x³ + 45x² + 100x + 6x² + 54x + 120 - 24

= x⁴ + 14x³ + 71x² + 100x + 96

Answer 3

(x + 2)(x + 3)(x + 4)(x + 5) – 24 =  (x + 2)(x + 5)(x + 4)(x + 3) – 24 

                                                            = ( x² + 7x +10) ( x² + 7x +12) – 24  đặt x² + 7x +10 = a

                                                            = a(a + 2 ) – 24 = a² + 2a – 24  = a² + 2a +1 – 25

                                                            = (a – 4 )( a + 6) 

Thay vào ta có: (x + 2)(x + 3)(x + 4)(x + 5) – 24  =  ( x² + 7x +6) ( x² + 7x +16)

                                                                              = (x + 6)(x + 1)( x² + 7x +16)