Đáp án:
$a) P(x)=x+3\\
Q(x)=3x+4\\
b) P(x)=0\\
\Leftrightarrow x=-3\\
Q(x)=0\\
\Leftrightarrow x=\frac{4}{3}\\
c) P(x)+Q(x)=4x+7\\
P(x)-Q(x)=-2x-1$
Giải thích các bước giải:
$a)P(x) + (2x^3 - 4x^2 + x - 10) = 2x^3 - 4x^2 + 2x - 7\\
\Rightarrow P(x)=2x^3 - 4x^2 + 2x - 7-(2x^3 - 4x^2 + x - 10)\\
=2x^3 - 4x^2 + 2x - 7-2x^3 + 4x^2 - x + 10\\
=(2x^3-2x^3)+(-4x^2+4x^2)+(2x-x)+(-7+10)\\
=x+3\\
Q(x) - (9x^3 +8x^2 - 2x -7) = -9x^3 - 8x^2 +5x +11\\
\Rightarrow Q(x)=-9x^3 - 8x^2 +5x +11+9x^3 +8x^2 - 2x -7\\
=(-9x^3+9x^3)+(-8x^2+8x^2)+(5x-2x)+(11-7)\\
=3x+4\\
b) P(x)=0\\
\Leftrightarrow x+3=0\\
\Leftrightarrow x=-3\\
Q(x)=0\\
\Rightarrow 3x+4=0\\
\Leftrightarrow x=\frac{4}{3}\\
c) P(x)+Q(x)=x+3+3x+4=4x+7\\
P(x)-Q(x)=x+3-3x-4=-2x-1$
