Question

What must be added 5x³-2x²+3x+7 to get 7x³+7x-5​

Answer 1

`\dashrightarrow \: { \tt{-(5 {x}^(3) - 2 {x}^(2) + 3x + 7) + ( {7x}^(3) + 7x - 5) }} \\ \\ \dashrightarrow \: { \tt{(7-5) {x}^(3) + 2 {x}^(2) + (7-3)x + (-5-7) }} \\ \\ \dashrightarrow \: { \tt{ {2x}^(3) +2 {x}^(2) + 4x -12}}`

Answer 2

Let the adding polynomial be y

`\\ \sf\longmapsto (5 {x}^(3) - 2 {x}^(2) + 3x + 7) + y = {7x}^(3) + 7x + 5 \\ \\ \sf\longmapsto {5x}^(3) - 2 {x}^(2) + 3x + 7 + y = {7x}^(3) + 7x + 5 \\ \\ \sf\longmapsto y = 7x {}^(3) - {5x}^(3) + 2x {}^(2) + 7x - 3x + 5 - 7 \\ \\ \sf\longmapsto {2x}^(3) + {2x}^(2) + 4x - 2`