Đáp án:
$\\$
`a,`
$\bullet$ `F (x) = 4x^3 - 1/2x + 8x^4 - 2x^3 + 5`
`-> F (x) = (4x^3 - 2x^3) - 1/2x + 8x^4 + 5`
`-> F (x) = 2x^3 - 1/2x + 8x^4 + 5`
Sắp xếp `F (x)` theo lũy thừa giảm dần của biến :
`F (x) = 8x^4 + 2x^3 - 1/2x + 5`
$\bullet$ `G (x) = -8x^4 + 7x + 8x^3 + 1/5 -10x^3`
`-> G (x) = -8x^4 + 7x + (8x^3-10x^3) + 1/5`
`-> G (x) =-8x^4 + 7x - 2x^3 + 1/5`
`-> G (x) = -8x^4 - 2x^3 + 7x + 1/5`
$\\$
`b,`
$\bullet$ `H (x) = F (x) + G (x)`
`-> H (x) = ( 8x^4 + 2x^3 - 1/2x + 5) + (-8x^4 - 2x^3 + 7x + 1/5)`
`-> H (x) = 8x^4 + 2x^3 - 1/2x + 5 -8x^4 - 2x^3 + 7x + 1/5`
`-> H (x) = (8x^4 - 8x^4) + (2x^3 - 2x^3) + (-1/2x + 7x) + (5+1/5)`
`-> H (x) = 13/2x + 26/5`
$\bullet$ `P (x) = F (x) - G (x)`
`-> P (x) = ( 8x^4 + 2x^3 - 1/2x + 5) - (-8x^4 - 2x^3 + 7x + 1/5)`
`-> P (x) = 8x^4 + 2x^3 - 1/2x + 5 + 8x^4 + 2x^3 - 8x - 1/5`
`-> P (x) = (8x^4 + 8x^4) + (2x^3 + 2x^3) + (-1/2x - 8x) + (5-1/5)`
`-> P (x) = 16x^4 + 4x^3 -15/2x +24/5`
