x^5+2x^4+2x^3+2x^2+2x+1

=(x^5+x^4)+(x^4+x^3)+(x^3+x^2)+(x^2+x)+(x+1)

=x^4(x+1)+x^3(x+1)+x^2(x+1)+x(x+1)+(x+1)

=(x+1)(x^4+x^3+x^2+x+1)

Câu a :

\(\dfrac{3x^2-12x+12}{x^4-8x}\)

\(=\dfrac{3\left(x^2-4x+4\right)}{x\left(x^3-8\right)}\)

\(=\dfrac{3\left(x-2\right)^2}{x\left(x-2\right)\left(x^2+2x+4\right)}\)

\(=\dfrac{3\left(x-2\right)}{x\left(x^2+2x+4\right)}\)

Câu b :

\(\dfrac{7x^2+14x+7}{3x^2+3x}\)

\(=\dfrac{7\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)}{3x}\)

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

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

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

d)\(x^8+3x^4+4=\left(x^8+4x^4+4\right)-x^4=\left(x^4+2\right)^2-\left(x^2\right)^2\)

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

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

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

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

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

a)\(x^2-x-12\)

\(=x^2+4x-3x-12\)

\(=x\left(x+4\right)-3\left(x+4\right)\)

\(=\left(x+4\right)\left(x-3\right)\)

b) \(x^2+8x+15\)

\(=x^2+3x+5x+15\)

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

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

A,          m²-7m+12=m²-3m+12-4m=m(m-3)-4(m-3)=(m-4)(m-3)

B,           2x⁴-x³+27-54x=x³(2-x)-27(2-x)=(x³-27)(2-x)=(x-3)(x²+3x+9)(2-x)

a) m^2 -7m +12 = m^2 -3m -4m +12

=m(m -3)-4 (m- 3)

=(m-4)(m-3)

b) 2x^4-x^3 -54x+ 27

=(2m^4-x^3)- (54x - 27)

=x^3(2x-1)-27(2x-1)

=(x^3-27)(2x-1)

a,(m-4)(m-3)

b,(x-3)(2x-1)(x^2-3x+9)

\(3x^4-48\)

\(=\left(3x^4-6x^3\right)+\left(6x^3-12x^2\right)+\left(12x^2-24x\right)+\left(24x-48\right)\)

\(=3x^3\left(x-2\right)+6x^2\left(x-2\right)+12x\left(x-2\right)+24\left(x-2\right)\)

\(=\left(x-2\right)\left[\left(3x^3+6x^2\right)+\left(12x+24\right)\right]\)

\(=\left(x-2\right)\left[3x^2\left(x+2\right)+12\left(x+2\right)\right]\)

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

\(x^4-8x\)

\(=x\left(x^3-8\right)\)

\(=x\left[\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(4x-8\right)\right]\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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