Đáp án:
$a)
2x^2+x+1\\
b)
x^2+1\\
c)
x+3$
Giải thích các bước giải:
$a)
(2x^4-5x^2+x^3-3-3x):(x^2-3)\\
=(2x^4+x^3+x^2-6x^2-3x-3):(x^2-3)\\
=\left [ x^2(2x^2+x+1)-3(2x^2-x-1) \right ]:(x^2-3)\\
=\left [ (2x^2+x+1)(x^2-3) \right ]:(x^2-3)\\
=2x^2+x+1\\
b)
(x^5+x^3+x^2+1):(x^3+1)\\
=\left [ x^2(x^3+1)+(x^3+1) \right ]:(x^3+1)\\
=\left [ (x^3+1)(x^2+1) \right ]:(x^3+1)\\
=x^2+1\\
c)
(2x^3+5x^2-2x+3):(2x^2-x+1)\\
=\left [ 2x^3+6x^2-x^2-3x+x+3 \right ]:(2x^2-x+1)\\
=\left [ 2x^2(x+3)-x(x+3)+(x+3) \right ]:(2x^2-x+1)\\
=\left [ (x+3)(2x^2-x+1) \right ]:(2x^2-x+1)\\
=x+3$
