Đáp án:
$a)
P(x)=-5x^3+3x^2+2x+5\\
Q(x)=-5x^3+6x^2+2x+5\\
b)
\Rightarrow P(1)+Q(1)=13\\
c) x=0$
Giải thích các bước giải:
$a)
P(x)=15-4x^3+3x^2+2x-x^3-10\\
=(-4x^3-x^3)+3x^2+2x+(15-10)\\
=-5x^3+3x^2+2x+5\\
Q(x)=5+4x^3+6x^2-5x-9x^3+7x\\
=(4x^3-9x^3)+6x^2+(-5x+7x)+5\\
=-5x^3+6x^2+2x+5\\
b)
P(x)+Q(x)=-5x^3+3x^2+2x+5+(-5x^3+6x^2+2x+5)\\
=-5x^3+3x^2+2x+5-5x^3+6x^2+2x+5\\
=(-5x^3-5x^3)+(3x^2+6x^2)+(2x+2x)+(5+5)\\
=-10x^3+9x^2+4x+10\\
\Rightarrow P(1)+Q(1)=-10.1^3+9.1^2+4.1+10=-10+9+4+10=13\\
c) Q(x)-P(x)=-5x^3+6x^2+2x+5-(-5x^3+3x^2+2x+5)\\
=-5x^3+6x^2+2x+5+5x^3-3x^2-2x-5\\
=(-5x^3+5x^3)+(6x^2-3x^2)+(2x-2x)+(5-5)\\
=3x^2\\
\Rightarrow Q(x)-P(x)=0\\
\Leftrightarrow 3x^2=0\\
\Leftrightarrow x=0$
