#Mon
a) F(x) + H(x) = G(x)
H(x) = G(x) - F(x)
H(x)= ($x^{4}$ - $x^{3}$ + $x^{2}$ +5) - ($x^{4}$ - 3$x^{2}$ +x -1)
= $x^{4}$ - $x^{3}$ + $x^{2}$ + 5 - $x^{4}$ + 3$x^{2}$ -x + 1
= ($x^{4}$ - $x^{4}$) - $x^{3}$ + ($x^{2}$ + 3$x^{2}$) - x + (5+1)
= -$x^{3}$ + 4$x^{2}$ - x + 6
b) F(x) - H(x) = G(x)
H(x) = F(x) - G(x)
H(x) = ($x^{4}$ - 3$x^{2}$ +x -1) - ($x^{4}$ - $x^{3}$ + $x^{2}$ +5)
= $x^{4}$ - 3$x^{2}$ +x -1 - $x^{4}$ + $x^{3}$ - $x^{2}$ - 5
= ($x^{4}$ - $x^{4}$) + (-3$x^{2}$ - $x^{2}$) + $x^{3}$ + x +(-1 -5)
= -4$x^{2}$ + $x^{3}$ x + (-6)
c) H(x) - G(x) = F(x)
H(x) = F(x) + G(x)
H(x) = ($x^{4}$ - 3$x^{2}$ +x -1) + ($x^{4}$ - $x^{3}$ + $x^{2}$ +5)
= $x^{4}$ - 3$x^{2}$ +x -1 + $x^{4}$ - $x^{3}$ + $x^{2}$ +5
= ($x^{4}$ + $x^{4}$) + (-3$x^{2}$ + $x^{2}$) - $x^{3}$ + x + (-1+5)
= 2$x^{4}$ + (-2$x^{2}$) - $x^{3}$ + x + 4
