Đáp án + Giải thích các bước giải:
a, `(2x^5 - 5x^3 + x^2 + 3x - 1) : (x^2 - 1)`
` = ( 2x^5 - 2x^3 - 3x^3 + x^2 + 3x - 1) : (x^2 - 1)`
` = [ (2x^5 - 3x^3 + x^2) - (2x^3 - 3x + 1)] : (x^2 - 1)`
` = [ x^2(2x^3 - 3x + 1) - (2x^3 - 3x + 1)] : (x^2 - 1)`
` = (x^2 - 1)(2x^3 - 3x + 1) : (x^2 - 1)`
` = 2x^3 - 3x + 1`
b, `(5x^5 - 2x^4 - 9x^3 + 7x^2 - 18x - 3) : (x^2 - 3)`
` = (5x^5 - 2x^4 - 15x^3 + 6x^3 + 6x^2 + x^2 - 18x - 3) : (x^2 - 3)`
` = [ (5x^5 - 2x^4 + 6x^3 + x^2) - (15x^3 - 6x^2 + 18x + 3)] : (x^2 - 3)`
` = [ x^2(5x^3 - 2x^2 + 6x + 1) - 3(5x^3 - 2x^2 + 6x + 1)] : (x^2 - 3)`
` = (x^2 - 3)(5x^3 - 2x^2 + 6x + 1) : (x^2 - 3)`
` = 5x^3 - 2x^2 + 6x + 1`
