x³ ​- 3x² - 9x - 5 = (x³ - 5x²) + (2x² -10x) + (x - 5) = x² (x - 5) + 2x(x - 5) + (x - 5) = (x - 5)(x²  + 2x + 1) = (x - 5)(x + 1)²

x^3-3x^2-9x-5

=x^3-5x^2+2x^2-10x+x-5

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

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

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

=x^3-3x+3-1

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

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

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

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

\(\dfrac{1}{2}x^3+4\)

\(=\dfrac{x^2+8}{2}\)

\(=\text{(x+2)(x^2 −2x+4)}\)

Nham nghiem thi ta thay pt co 1 ngiem x=2/3

=> tach nhu sau :

\(3x^3-2x^2-3x^2+2x+3x-2\) 

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

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

Chuc ban hoc tot

\(x^2-4y^2+16x+64=\left(x^2+16x+64\right)-4y^2\)

\(=\left(x+8\right)^2-\left(2y\right)^2\)

\(=\left(x-2y+8\right)\left(x+2y+8\right)\)

1/(x+2)² -(3x-1)²=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x²+12x

2/(x⁴+x²)(-2x³-2x)=x²(x²+1)-2x(x²+1)=(x²+1)(x²-2x)

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

\(3x^4-5x^3-18x^2-3x+5\)

\(=3x^4-6x^3+x^3-15x^2-2x^2-x^2-5x+2x+5\)\(=\left(3x^4-6x^3-15x^2\right)+\left(x^3-2x^2-5x\right)-\left(x^2-2x-5\right)\)

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

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

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

\(=x^3+x^2-3x^2-4x-1+7x-x^2\)

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

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