d,Sửa đề

\(-x^3+6x^2-12x+8\)

\(=-\left(x^3-6x^2+12x-8\right)\)

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

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

\(e,27x^3+81x^2+81x+27\)

\(=27\left(x^3+3x^2+3x+1\right)\)

\(=27\left(x+1\right)^3\)

a.

\(\Leftrightarrow\sqrt[3]{3x-5}=\left(2x-3\right)^3+2x-3-\left(3x-5\right)\)

Đặt \(\left\{{}\begin{matrix}2x-3=a\\\sqrt[3]{3x-5}=b\end{matrix}\right.\)

\(\Rightarrow b=a^3+a-b^3\)

\(\Leftrightarrow a^3-b^3+a-b=0\)

\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+1\right)=0\)

\(\Leftrightarrow a=b\)

\(\Leftrightarrow\sqrt[3]{3x-5}=2x-3\)

\(\Leftrightarrow3x-5=\left(2x-3\right)^3\)

\(\Leftrightarrow8x^3-36x^2+51x-22=0\)

\(\Leftrightarrow\left(x-2\right)\left(8x^2-20x+11\right)=0\)

\(\Leftrightarrow...\)

b.

\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x+3x-2-\sqrt[3]{81x-8}=0\)

\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x+\dfrac{\left(3x-2\right)^3-\left(81x-8\right)}{\left(3x-2\right)^2+\left(3x-2\right)\sqrt[3]{81x-8}+\sqrt[3]{\left(81x-8\right)^2}}=0\)

\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x+\dfrac{27\left(x^3-2x^2-\dfrac{5}{3}x\right)}{\left(3x-2\right)^2+\left(3x-2\right)\sqrt[3]{81x-8}+\sqrt[3]{\left(81x-8\right)^2}}=0\)

\(\Leftrightarrow\left(x^3-2x^2-\dfrac{5}{3}x\right)\left(1+\dfrac{27}{\left(3x-2\right)^2+\left(3x-2\right)\sqrt[3]{81x-8}+\sqrt[3]{\left(81x-8\right)^2}}\right)=0\)

\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x=0\)

17) \(8x^3+27=\left(2x\right)^3+3^3=\left(2x+3\right)\left(4x^2-6x+9\right)\)

18) \(a^6-1=\left(a^3\right)^2-1=\left(a^3-1\right)\left(a^3+1\right)=\left(a-1\right)\left(a^2+a+1\right)\left(a+1\right)\left(a^2-a+1\right)\)

20) \(9x^4-81x^2=9\left(x^4-9x^2\right)=9x^2\left(x^2-9\right)=9x^2\left(x-3\right)\left(x+3\right)\)

17)

\(8x^3+27=\left(8x\right)^3+3^3=\left(8x+3\right)\left(64x^2-24x+9\right)\)

18)

\(a^6-1=\left(a^3\right)^2-1\)

\(=\left(a^3-1\right)\left(a^3+1\right)\)

\(=\left(a-1\right)\left(a^2-a+1\right)\left(a+1\right)\left(a^2+a+1\right)\)

19)

đề sao sao ý

20)

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

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

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

1, \(x^3+8x^2+17x+10=\left(x^3+x^2\right)+\left(7x^2+7x\right)+\left(10x+10\right)\)

\(=x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)\)\(=\left(x+1\right)\left(x^2+7x+10\right)=\left(x+1\right)\left(x+2\right)\left(x+5\right)\)

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

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

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

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

4. \(81x^4+4=\left(9x^2\right)^2+2^2=\left(9x^2+2\right)^2-2.9x^2.2=\left(9x^2+2\right)^2-\left(6x\right)^2\)

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

1/\(9x^2+6x-575=\left(3x\right)^2+2.3x.1+1-576=\left(3x+1\right)^2-24^2=\left(3x-23\right)\left(3x+25\right)\)

2/\(81x^4+4=81x^4+36x^2+4-36x^2=\left(9x^2+2\right)^2-\left(6x\right)^2\)

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

3/đặt \(t=x^2+8x+7\) thì đa thức cần phân tích:

t(t+8)+15=t²+8t+15=t²+3t+5t+15=t(t+3)+5(t+3)=(t+3)(t+5)=(x²+8x+10)(x²+8x+12)=(x²+8x+10)(x²+2x+6x+12)

=(x²+8x+10)[x(x+2)+6(x+2)]=(x²+8x+10)(x+2)(x+6)

tạm thế này đã, phải đi ăn cơm rồi :v

giúp mình nốt 4,5 nha

Nhiều qua trời 

a/ 2x³ ‐5x² + 8x ‐3

= 2x³ ‐x² ‐4x² +2x +6x ‐3

= x² (2x‐1) ‐ 2x(2x‐1) + 3.(2x‐1)

= (x²‐2x+3) (2x‐1) 

b/ 3x³ ‐ 14x² +4x +3

= 3x³ +x² ‐15 x² ‐5x +9x +3

= x²(3x+1) ‐5.x (3x+1) +3. (3x+1) 

= (x² ‐5x+3) (3x+1) 

8x(x+y)-x-y=(8x-1)(x+y)

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

81x^2y^2 -25= (9xy)^2 -5^2 = (9xy-5)(9xy+5)

27x^3 -1 = (3x)^3 -1 = (3x-1)(9x+3x+1)

\(81x^2y^2-25=\left(9xy-5\right)\left(9xy+5\right)\)

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

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