Đáp án:
$a)P(x)+Q(x)=2x^2-2x\\
b)
P(x)-Q(x)=2x^3+4x^2+8x-4\\
c)
{\left[\begin{aligned}x=0\\x=1 \end{aligned}\right.}$
Giải thích các bước giải:
$a)P(x)+Q(x)=x^3+3x^2+3x-2+(-x^3-x^2-5x+2)\\
=x^3+3x^2+3x-2-x^3-x^2-5x+2\\
=(x^3-x^3)+(3x^2-x^2)+(3x-5x)+(-2+2)\\
=2x^2-2x\\
b)
P(x)-Q(x)=x^3+3x^2+3x-2-(-x^3-x^2-5x+2)\\
=x^3+3x^2+3x-2+x^3+x^2+5x-2\\
=(x^3+x^3)+(3x^2+x^2)+(3x+5x)+(-2-2)\\
=2x^3+4x^2+8x-4\\
c)
H(x)=0\\
\Leftrightarrow P(x)+Q(x)=0\\
\Leftrightarrow 2x^2-2x=0\\
\Leftrightarrow 2x(x-1)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=1 \end{aligned}\right.}$