a)\(P\left(x\right)=x^4+5+x^2-15x^3-9x-12\)
\(P\left(x\right)=x^4-15x^3-9x-7\)
Hệ số cao nhất : 1
Hệ số tự do : -7
\(Q\left(x\right)=-3x^4-x^3+2x^2-4x-4+4x^4-x^2\)
\(Q\left(x\right)=x^4-x^3+x^2-4x-4\)
Hệ số cao nhất : 1
hệ số tự do : -4
b)\(P\left(-1\right)=\left(-1\right)^4-15.\left(-1\right)^3-9.\left(-1\right)-7\)
\(P\left(-1\right)=1+15+9-7=18\)
\(Q\left(1\right)=1^4-1^3+1^2-4.1-4\)
\(Q\left(1\right)=1-1+1-4-4=-7\)
c)\(H\left(x\right)=P\left(x\right)+Q\left(x\right)\)
\(H\left(x\right)=x^4-15x^3-9x-7+x^4-x^3+x^2-4x-4\)
\(H\left(x\right)=2x^4-16x^3+x^2-13x-11\)
\(G\left(x\right)=P\left(x\right)-3.Q\left(x\right)\)
\(G\left(x\right)=x^4-15x^3-9x-7-3\left(x^4-x^3+x^2-4x-4\right)\)
\(G\left(x\right)=x^4-15x^3-9x-7-3x^4+3x^3-3x^2+12x+12\)
\(G\left(x\right)=-2x^4-12x^3-3x^2+3x+5\)
