Question

Answer 1

a/\(A\left(x\right)-B\left(x\right)=\left(3x^4-3x^2+6x\right)-\left(x^2-2x^4+3\right)\)
\(=3x^4-3x^2+6x-x^2+2x^4-3\)
\(=\left(3x^4+2x^4\right)-\left(3x^2+x^2\right)+6x-3\)
\(=6x^4-4x^2+6x-3\)
b/\(C\left(x\right)-2B\left(x\right)=\left(x^2+3x-2\right)-2\left(x^2-2x^4+3\right)\)
\(=x^2+3x-2-2x^2+4x^4-6\)
\(=\left(x^2-2x^2\right)+3x+4x^4-\left(2+6\right)\)
\(=-x^2+3x+4x^4-8\)
c/\(3A\left(x\right)-C\left(x\right)=3\left(3x^4-3x^2+6x\right)-\left(x^2+3x-2\right)\)
\(=9x^4-9x^2+18x-x^2-3x+2\)
\(=9x^4-\left(9x^2+x^2\right)+\left(18x-3x\right)+2\)
\(=9x^4-10x^2+15x+2\)