a, \(6x^2-xy-y^2\)

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

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

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

b, \(8x^2-23x-3\)

\(=8x^2-24x+x-3\)

\(=8x\left(x-3\right)+\left(x-3\right)=\left(8x+1\right)\left(x-3\right)\)

c, \(10x^2-11x-6\)

\(=10x^2-15x+4x-6\)

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

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

d, \(x^3-6x^2+11x-6\)

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

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

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

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

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

a)

\(x^3+6x^2+11x+6=(x^3-x)+(6x^2+12x+6)\)

\(=x(x^2-1)+5(x^2+2x+1)\)

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

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

\(=(x+1)(x^2+2x+3x+6)\)

\(=(x+1)[x(x+2)+3(x+2)]=(x+1)(x+2)(x+3)\)

b) \(x^3+6x^2-13x-42\)

\(=x^3+2x^2+4x^2+8x-21x-42\)

\(=x^2(x+2)+4x(x+2)-21(x+2)\)

\(=(x+2)(x^2+4x-21)\)

\(=(x+2)[x^2-3x+7x-21)\)

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

c)

\(x^3-5x^2+8x-4=(x^3-x^2)-4x^2+8x-4\)

\(=x^2(x-1)-4(x^2-2x+1)\)

\(=x^2(x-1)-4(x-1)^2\)

\(=(x-1)[x^2-4(x-1)]=(x-1)(x^2-4x+4)\)

\(=(x-1)(x-2)^2\)

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

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

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

\(=2x^2(x+1)-3[x^2+x-2x-2]\)

\(=2x^2(x+1)-3[x(x+1)-2(x+1)]\)

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

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

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

\(x^3+3.x^2.2+3.x.2^2+2^2-x+2=\left(x+2\right)^3-\left(x+2\right)=\left(x+2\right)\left(\left(x-2\right)^2-1\right)\)

x³+6x²+11x+6

= x³+3x²+3x²+9x+2x+6

=x²(x+3)+ 3x(x+3)+2(x+3)

=(x+3)(x²+3x+2)

a, \(x^4-6x^3+11x^2-6x+1=0\)

\(\Rightarrow\left(x^2-3x+1\right)^2=0\)

\(\Rightarrow x^2-3x+1=0\)

\(\Rightarrow x=\frac{\pm\sqrt{5}+3}{2}\)

Chúc bạn học tốt

\(x^4-\left(6x^2-2x^2\right)+\left(9x^2-6x+1\right)=0\)

\(x^4-2x^2\left(3x-1\right)+\left(3x-1\right)^2=0\)

\(\left(x^2-3x+1\right)^2=0\)

tự làm

B) \(\left(6x^4-18x^3\right)+\left(13x^{^3}-39x^2\right)+\left(x-3x\right)-\left(2x-6\right)=0\)

\(6x^3\left(x-3\right)+13x^2\left(x-3\right)+x\left(x-3\right)-2\left(x-3\right)=0\)

\(\left(x-3\right)\left(6x^3+13x^2-2\right)=0\)

\(\left(x-3\right)\left(6x^3+12x^2+x^2+2x-x-2\right)\)

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

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

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

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

\(\left(x-3\right)\left(x+2\right)\left(2x-1\right)\left(3x+1\right)=0\)

câu C nghĩ đã

a, \(x^4-6x^3+11x^2-6x+1=0\)

=> \(x^4-6x^3+9x^2+2x^2-6x+1=0\)

=> \(x^2+3x+1=0\)

=> \(\Delta\) =\(b^2-4c\)

=\(3^2.4=5\)

Nên \(\sqrt{\Delta}=5\)

x= \(\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-3+\sqrt{5}}{2}\)

hoặc x= \(\dfrac{b+\sqrt{\Delta}}{2a}=\dfrac{3+\sqrt{5}}{2}\)

Đáp án câu a.

https://giaibaitapvenha.blogspot.com/2017/12/toan-lop-8-ai-so_27.html

a)

\(x^3-7x-6=x^3-x-6x-6\)

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

\(=x(x-1)(x+1)-6(x+1)=(x+1)[x(x-1)-6]\)

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

\(=(x+1)[x(x-3)+2(x-3)]=(x+1)(x+2)(x-3)\)

b) \(x^3-6x^2+8x\)

\(=x(x^2-6x+8)\)

\(=x(x^2-4x-2x+8)\)

\(=x[x(x-4)-2(x-4)]=x(x-2)(x-4)\)

c) \(x^4+2x^3-16x^2-2x+15\)

\(=(x^4+2x^3-x^2-2x)-15x^2+15\)

\(=[(x^4-x^2)+(2x^3-2x)]-15(x^2-1)\)

\(=[x^2(x^2-1)+2x(x^2-1)]-15(x^2-1)\)

\(=(x^2-1)(x^2+2x)-15(x^2-1)=(x^2-1)(x^2+2x-15)\)

\(=(x^2-1)(x^2-3x+5x-15)=(x^2-1)[x(x-3)+5(x-3)]\)

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

d)

\(x^3-11x^2+30x=x(x^2-11x+30)\)

\(=x(x^2-5x-6x+30)\)

\(=x[x(x-5)-6(x-5)]=x(x-6)(x-5)\)

\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)

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

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

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

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