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a)f(x)+h(x)=g(x)=>h(x)=g(x)-f(x)
g(x)-f(x)=(x4-x3+x2+5)-(x4-3x2+x-1)
=x4-x3+x2+5-x4+3x2-x+1
=(x4-x4)-x3+(x2+3x2)-x+(5+1)
=-x3+4x2-x+6
b) f(x)-h(x)=g(x)
=>h(x)=f(x)-g(x)
f(x)-g(x)=(x4-3x2+x-1)-(x4-x3+x2+5)
=x4-3x2+x-1-x4+x3-x2-5
=(x4-x4)+x3+(-3x2-x2)+x+(-1-5)
=x3-4x2+x-6
a) f(x) - g(x) - h(x) = (x3-2x2+3x+1)-(x3+x-1)-(2x2-1)
=x3- 2x2+3x + 1 -x3-x+1 - 2x2+1
= ( x3-x3)+(-2x2-2x2) + (3x-x)+(1 + 1 + 1 )
= -4x2 + 2x +3
a)+)\(f\left(x\right)=3x^4-5x^3-x^2+1007\)
\(\Rightarrow f\left(x\right)=\left(3x^2-5x-1\right)x^2+1007\)
+)\(g\left(x\right)=2x^4+3x^3-1007\)
\(\Rightarrow g\left(x\right)=\left(2x^2+3x\right)x^2-1007\)
\(\Rightarrow f\left(x\right)-g\left(x\right)-2014=\left[\left(3x^2-5x-1\right)x^2+1007\right]-\left[\left(2x^2+3x\right)x^2-1007\right]-2014\)
\(f\left(x\right)-g\left(x\right)-2014=\left(3x^2-5x-1\right)x^2+1007-\left(2x^2+3x\right)x^2+1007-2014\)
\(f\left(x\right)-g\left(x\right)-2014=\left[\left(3x^2-5x-1\right)-\left(2x^2+3x\right)\right]x^2+\left(1007+1007-2014\right)\)
\(f\left(x\right)-g\left(x\right)-2014=3x^2-5x-1-2x^2-3x\)
\(\Rightarrow f\left(x\right)-g\left(x\right)-2014=x^2-2x-1=\left(x-1\right)^2\)
b)\(2014+g\left(x\right)-h\left(x\right)=f\left(x\right)\)
\(\Rightarrow-h\left(x\right)=f\left(x\right)-g\left(x\right)-2014\)
\(\Rightarrow-h\left(x\right)=\left(x-1\right)^2\)
\(\Rightarrow h\left(x\right)=-\left[\left(x-1\right)^2\right]\)
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