Đáp án:
$4B)\\
P(x)+Q(x)+H(x)=2x^3+x^2+4x-15\\
P(x)+Q(x)-H(x)=-2x^3-x^2+4x-13\\
5B)\\
a) P(x)+Q(x)=3x^3-4x^2+3x+1\\
P(x)-Q(x)=x^3-2x^2-x-1\\
b)
P(x)-2Q(x)=-x^2-3x-2\\
P(x)+3Q(x)=5x^3-6x^2+7x+3\\$
Giải thích các bước giải:
$4B)\\
P(x)+Q(x)+H(x)=x^3-2x^2+x-5-x^3+2x^2+3x-9+2x^3+x^2-1\\
=(x^3-x^3+2x^3)+(-2x^2+2x^2+x^2)+(x+3x)+(-5-9-1)\\
=2x^3+x^2+4x-15\\
P(x)+Q(x)-H(x)=x^3-2x^2+x-5-x^3+2x^2+3x-9-(2x^3+x^2-1)\\
=x^3-2x^2+x-5-x^3+2x^2+3x-9-2x^3-x^2+1\\
=(x^3-x^3-2x^3)+(-2x^2+2x^2-x^2)+(x+3x)+(-5-9+1)\\
=-2x^3-x^2+4x-13\\
5B)\\
a) P(x)+Q(x)=2x^3-3x^2+x+x^3-x^2+2x+1\\
=(2x^3+x^3)+(-3x^2-x^2)+(x+2x)+1\\
=3x^3-4x^2+3x+1\\
P(x)-Q(x)=2x^3-3x^2+x-(x^3-x^2+2x+1)\\
=2x^3-3x^2+x-x^3+x^2-2x-1\\
=(2x^3-x^3)+(-3x^2+x^2)+(x-2x)-1\\
=x^3-2x^2-x-1\\
b)
P(x)-2Q(x)=2x^3-3x^2+x-2(x^3-x^2+2x+1)\\
=2x^3-3x^2+x-2x^3+2x^2-4x-2\\
=(2x^3-2x^3)+(-3x^2+2x^2)+(x-4x)-2\\
=-x^2-3x-2\\
P(x)+3Q(x)=2x^3-3x^2+x+3(x^3-x^2+2x+1)\\
=2x^3-3x^2+x+3x^3-3x^2+6x+3\\
=(2x^3+3x^3)+(-3x^2-3x^2)+(x+6x)+3\\
=5x^3-6x^2+7x+3\\$
