a)\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b)\(\left(x-3\right)\left(x-7\right)\left(x+2\right)\)
c)\(\left(x-3\right)\left(x+3\right)\left(x+2\right)\left(x+1\right)\)
d)\(\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
a) x3 + 6x2 + 11x + 6
= (x3 + x2) + (5x2 + 5x) + (6x + 6)
= x2(x + 1) + 5x(x + 1) + 6(x + 1)
= (x2 + 5x + 6)(x + 1)
= (x2 + 2x + 3x + 6)(x + 1)
= [x(x + 2) + 3(x + 2)](x + 1)
= (x + 3)(x + 2)(x + 1)
b) x3 - 8x2 + x + 42
= x3 + 2x2 - 10x2 - 20x + 21x + 42
= x2(x + 2) - 10x(x + 2) + 21(x + 2)
= (x2 - 10x + 21)(x + 2)
= (x2 - 3x - 7x + 21)(x + 2)
=[x(x - 3) - 7(x - 3)](x + 2)
=(x - 7)(x - 3)(x + 2)
c) x4 + 3x3 - 7x2 - 27x - 18
= x4 + x3 + 2x3 + 2x2 - 9x2 - 9x - 18x - 18
= x3(x + 1) + 2x2(x + 1) - 9x(x + 1) - 18(x + 1)
= (x3 + 2x2 - 9x - 18)(x + 1)
= [x2(x + 2) - 9(x + 2)](x + 1)
=(x2 - 9)(x + 2)(x + 1)
= (x - 3)(x + 3)(x + 2)(x + 1)
d) x4 + 5x3 - 7x2 - 41x - 30
= x4 + x3 + 4x3 + 4x2 - 11x2 - 11x - 30x - 30
= x3(x + 1) + 4x2(x + 1) - 11x(x + 1) -30(x + 1)
= (x3 + 4x2 - 11x - 30)(x + 1)
= (x3 + 2x2 + 2x2 + 4x - 15x - 30)(x + 1)
= [x2(x + 2) + 2x(x + 2) - 15(x +2)](x + 1)
=(x2 + 2x - 15)(x + 2)(x + 1)
= (x2 - 3x + 5x - 15)(x + 2)(x +1)
= [x(x - 3) + 5(x - 3)](x + 2)(x + 1)
= (x - 3)(x + 5)(x + 2)(x + 1)
NHỚ TIK CHO MIK NHA, đừng có mà đọc suông xong bỏ đi đấy. mik là đầy đủ hơn cái bn ở dưới nên cho mik nhiều tik hơn nhé