(3x³ - 17x² + 15x - 25)/(x - 5) =
= (3x³ - 15x² - 2x² + 0x + 5x - 25)/(x - 5)
= [3x²(x - 5) - 2x(x - 5) + 5(x - 5)]/(x - 5)
= (3x² - 2x + 5)(x - 5)/(x - 5)
= 3x² - 2x + 5
(5x³ + 18x² + 7x - 6)/(x + 3) =
= (5x³ + 5x² + 13x² + 13x - 6x - 6³)/(x + 3)
= [5x²(x + 1) + 13x(x + 1) - 6(x + 1)]/(x + 3)
= (x + 1)(5x² + 13x - 6)/(x + 3)
= (x + 1)(5x² + 15x - 2x - 6)/(x + 3)
= (x + 1)[5x(x + 3) - 2(x + 3)]/(x + 3)
= (x + 1)(5x - 2)(x + 3)/(x + 3)
= (x + 1)(5x - 2)
(4x³ + 8x² - 9x - 18)/(x + 2) =
= [4x²(x + 2) - 9(x + 2)]/(x + 2)
= (4x² - 9)(x + 2)/(x + 2)
= (4x² - 9)
= (2x - 3)(2x + 3)
(9x³ - 16x - 18x² + 32)/(x - 2) =
= [x(9x² - 16) - 2(9x² - 16)]/(x - 2)
= (9x² - 16)(x - 2)/(x - 2)
= 9x² - 16
= (3x - 4)(3x + 4)
(- x³ + 75x - 250)/(x + 10) =
= ( - x³ + 5x² - 5x² + 25x + 50x - 250)/(x + 10)
= [ - x²(x -5) - 5x(x - 5) + 50(x - 5)]/(x + 10)
= - (x - 5)(x² + 10x - 5x - 50)/(x + 10)
= - (x - 5)[x(x + 10) - 5(x + 10)]/(x + 10)
= - (x - 5)(x - 5)(x + 10)/(x + 10)
= - (x - 5)²
(3x³ - 16x² - 72)/(x - 6) =
= (3x³ - 18x² + 2x² - 72)/(x - 6)
= [3x²(x - 6) + 2(x² - 36)]/(x - 6)
= [3x²(x - 6) + 2(x - 6)(x + 6)]/(x - 6)
= [3x² + 2(x + 6)](x - 6)/(x - 6)
= 3x² + 2x + 12
