c: \(x^3-8x^2+x+42\)

\(=x^3+2x^2-10x^2-20x+21x+42\)

\(=\left(x+2\right)\left(x^2-10x+21\right)\)

\(=\left(x+2\right)\left(x-3\right)\left(x-7\right)\)

a: \(x^3+6x^2+11x+6\)

\(=x^3+3x^2+3x^2+9x+2x+6\)

\(=\left(x+3\right)\left(x^2+3x+2\right)\)

\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

b) 3x⁴-3x³+9x³-9x²-24x²+24x-48x+48

=3x³(x-1)+9x²(x-1)-24x(x-1)-48(x-1)

=(x-1)(3x³+9x²-24x-48)

=3(x-1)(x³+3x²-8x-16)

a: x^3-7x-6

=x^3-x-6x-6

=x(x-1)(x+1)-6(x+1)

=(x+1)(x^2-x-6)

=(x-3)(x+2)(x+1)

b: =2x^3+x^2-2x^2-x+6x+3

=x^2(2x+1)-x(2x+1)+3(2x+1)

=(2x+1)(x^2-x+3)

c: =2x^3-3x^2-2x^2+3x+2x-3

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

=(2x-3)(x^2-x+1)

d: =2x^3+x^2+2x^2+x+2x+1

=(2x+1)(x^2+x+1)

e: =3x^3+x^2-3x^2-x+6x+2

=(3x+1)(x^2-x+2)

f: =27x^3-9x^2-18x^2+6x+12x-4

=(3x-1)(9x^2-6x+4)

a) \(x^3-7x-6\)

\(=x^3-x-6x-6\)

\(=\left(x^3-x\right)-\left(6x+6\right)\)

\(=x\left(x^2-1\right)-6\left(x+1\right)\)

\(=x\left(x+1\right)\left(x-1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

b) \(2x^3-x^2+5x+3\)

\(=2x^3+x^2-2x^2-x+6x+3\)

\(=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)

\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)

\(=\left(x^2-x+3\right)\left(2x+1\right)\)

c) \(2x^3-5x^2+5x+1\)

\(=2x^3-3x^2-2x^2+3x+2x-3\)

\(=\left(2x^3-3x^2\right)-\left(2x^2-3x\right)+\left(2x-3\right)\)

\(=x^2\left(2x-3\right)-x\left(2x-3\right)+\left(2x-3\right)\)

\(=\left(x^2-x+1\right)\left(2x-3\right)\)

d) \(2x^3+3x^2+3x+1\)

\(=2x^3+x^2+2x^2+x+2x+1\)

\(=\left(2x^3+x^2\right)+\left(2x^2+x\right)+\left(2x+1\right)\)

\(=x^2\left(2x+1\right)+x\left(2x+1\right)+\left(2x+1\right)\)

\(=\left(2x+1\right)\left(x^2+x+1\right)\)

e) \(3x^3-2x^2+5x+2\)

\(=3x^3+x^2-3x^2-x+6x+2\)

\(=\left(3x^3+x^2\right)-\left(3x^2+x\right)+\left(6x+2\right)\)

\(=x^2\left(3x+1\right)-x\left(3x+1\right)+2\left(3x+1\right)\)

\(=\left(3x-1\right)\left(x^2-x+2\right)\)

f) \(27x^3-27x^2+18x-4\)

\(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=\left(27x^3-9x^2\right)-\left(18x^2-6x\right)+\left(12x-4\right)\)

\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)

\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)

a) x^4+3x^3-7x^2-27x-18 = x^4+3x^3-3x^2-4x^2-9x-12x-6x-18

                                         = (x^4+3x^3)-(3x^2+9x)-(4x^2+12x)-(6x+18)

                                         = x^3*(x+3)-3x*(x+3)-4x*(x+3)-6(x+3)

                                         = ( x^3-3x-4x-6)*(x+3)

Những câu kia chưa tính ra

a) Ta có: \(x^4+3x^3-7x^2-27x-18\)

\(=x^4-3x^3+6x^3-18x^2+11x^2-33x+6x-18\)

\(=x^3\left(x-3\right)+6x^2\left(x-3\right)+11x\left(x-3\right)+6\left(x-3\right)\)

\(=\left(x-3\right)\left(x^3+6x^2+11x+6\right)\)

\(=\left(x-3\right)\left(x^3+x^2+5x^2+5x+6x+6\right)\)

\(=\left(x-3\right)\left[x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\right]\)

\(=\left(x-3\right)\left(x+1\right)\left(x^2+5x+6\right)\)

\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)\)

b) Ta có: \(x^3-8x^2+x+42\)

\(=x^3-7x^2-x^2+7x-6x+42\)

\(=x^2\left(x-7\right)-x\left(x-7\right)-6\left(x-7\right)\)

\(=\left(x-7\right)\left(x^2-x-6\right)\)

\(=\left(x-7\right)\left(x-3\right)\left(x+2\right)\)

c) Ta có: \(x^4+5x^3-7x^2-41x-30\)

\(=x^4+5x^3-7x^2-35x-6x-30\)

\(=x^3\left(x+5\right)-7x\left(x+5\right)-6\left(x+5\right)\)

\(=\left(x+5\right)\left(x^3-7x-6\right)\)

\(=\left(x+5\right)\left(x^3-x-6x-6\right)\)

\(=\left(x+5\right)\left[x\left(x^2-1\right)-6\left(x+1\right)\right]\)

\(=\left(x+5\right)\left[x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\right]\)

\(=\left(x+5\right)\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+5\right)\left(x+1\right)\left(x-3\right)\left(x+2\right)\)

a ) \(==>x^3.\left(x+3\right)-\left(7x^2+27x+18\right)\)

ko xét phần x^3.( x+3 ) nữa mà mik phân tích trong ngoặc nha zo thi ko lm như vậy mà ghi lại phần đó nha

\(7x^2+21x+6x+18\)

\(7x\left(x+3\right)+6\left(x+3\right)\)

\(\left(x+3\right)\left(7x+6\right)\)

==> \(x^3.\left(x+3\right)-\left(x+3\right)\left(7x+6\right)\)

==>\(\left(x+3\right)\left(x^3-7x-6\right)\)

\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)

\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)

\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)

\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)

\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)

\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)

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