a) x²+x-2
= x²-x+2x-2
= x(x-1)+2(x-1)
= (x+2)(x-1)
b) 2x²+5x+3
= 2x²+2x+3x+3
= 2x(x+1)+3(x+1)
= (2x+3)(x+1)
c) 3x²+5x-2
= 3x²+6x-1x-2
= 3x(x+2)-1(x+2)
= (3x-1)(x+2)

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

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

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

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

\(x^6-x^4+2x^3+2x^2\)

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

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

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

\(x-y=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)\)

a: \(x^4+3x^3+x^2+3x\)

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

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

c: \(x^2-xy-x+y\)

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

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

=3x(x+2y)

=3x(x+2y)

3x² + 6xy

= 3x(x+2y)

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

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

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

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

Tham Khảo

2x² + x - 6

= 2x² + 4x - 3x - 6

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

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

\(6x^2-13x+6\)

\(=6x^2-9x-4x+6\)

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

x²-2x-15=(x²-5x)+(3x-15)=x(x-5)+3(x-5)=(x-5)(x+3)

\(x^2-3x-15=\left(x^2-2.\dfrac{3}{2}x+\dfrac{9}{4}\right)-\dfrac{69}{4}=\left(x-\dfrac{3}{2}\right)^2-\left(\dfrac{\sqrt{69}}{2}\right)^2\)

\(=\left(x-\dfrac{3}{2}-\dfrac{\sqrt{69}}{2}\right)\left(x-\dfrac{3}{2}+\dfrac{\sqrt{69}}{2}\right)\)

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

\(3x^2-14x-5=3x\left(x-5\right)+\left(x-5\right)=\left(x-5\right)\left(3x+1\right)\)

\(3x^2-14x-5\)

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

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

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

A= 3x^2 + 14x - 15
3A= (3x)^2 + 2.7.(3x) - 15.3
3A= (3x+7)^2 +(15.3-7.7)
3A= (3x+7 )^2 -2^2
3A= (3x+7-2 )((3x+7+2 )
A= ( 3x-5)( x+ 3)