Làm tính chia:

$$\begin{gathered} a) (6x^3-7x^2-x+2) : (2x+1); \\ b) (x^4-x^3+x^2+3x) : (x^2-2x+3); \\ c) (x^2-y^2+6x+9):(x+y+3); \end{gathered}$$

Giải:

$a) (6x^3-7x^2-x+2) : (2x+1)$

$Vậy (6x^3-7x^2-x+2) : (2x+1)=3x^2–5x+2$

$b) (x^4-x^3+x^2+3x) : (x^2-2x+3)$

$Vậy (x^4-x^3+x^2+3x) : (x^2-2x+3)=x^2+x$

$$\begin{gathered} c) (x^2-y^2+6x+9):(x+y+3) \\ =(x^2+6x+9–y^2) : (x+y+3) \\ =[(x^2+2x.3+3^2)–y^2] : (x+y+3) \\ =[{(x+3)}^2–y^2] : (x+y+3) \\ =(x+3–y\left)\right(x+3+y):(x+y+3) \\ =x+3–y \\ =x–y+3 \end{gathered}$$