`a)`
`h(x)=f(x)+g(x)`
`=(5x^5+2x^4-x^2)+(-3x^2+x^4-1+5x^5)`
`=5x^5+2x^4-x^2-3x^2+x^4-1+5x^5`
`=(5x^5+5x^5)+(2x^4+x^4)+(-x^2-3x^2)-1`
`=10x^5+3x^4-4x^2-1`
``
`q(x)=f(x)-g(x)`
`=(5x^5+2x^4-x^2)-(-3x^2+x^4-1+5x^5)`
`=5x^5+2x^4-x^2+3x^2-x^4+1-5x^5`
`=(5x^5-5x^5)+(2x^4-x^4)+(-x^2+3x^2)+1`
`=x^4+2x^2+1`
`b)`
`h(1)=10.1^5+3.1^4-4.1^2-1=10+3-4-1=8`
`q(-1)=(-1)^4+2(-1)^2+1=1+2+1=4`
`c)`
`q(x)=x^4+2x^2+1`
Ta có:
`x^4 \ge0AAx`
`2x^2 \ge0AAx`
`\to x^4+2x^2+1 \ge1 \ne0`
Vậy `q(x)` vô nghiệm.
