Write this: x + 2)-2x³ + x² - 2x + 3 -2x³ divided by x give -2x². Write that above the + x² -2x² x + 2)-2x³ + x² - 2x + 3 -2x² times +2 gives -4x². Write that under the + x² -2x² x + 2)-2x³ + x² - 2x + 3 - 4x² -2x² times x gives -2x³. Write that under the -2x³: -2x² x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² Draw a line: -2x² x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² Subtract -2x³ - (-2x³), that gives 0 so we don't write anything under that. then x² minus -x² is really x²+4x² or 5x² -2x² x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² Bring down the - 2x -2x² x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² divided by x gives + 5x. Write that at the top after -2x² -2x² + 5x x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x times + 2 gives + 10x. Write that under the - 2x -2x² + 5x x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x + 10x 5x times x gives 5x². Write that under the 5x² -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x Draw a line: -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x Subtract 5x² - 5x², that gives 0 so we don't write anything under that. then -2x minus +10x is really -2x-10x or -12x -2x² + 5x x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x Bring down the + 3 -2x² + 5x x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x + 3 -12x divided by x give -12. Write that on the right at the top. -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x + 3 -12 times +2 gives -24. Write that under the +3 -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x + 3 - 24 -12 times x gives -12x -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x + 3 -12x - 24 Draw a line: -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x + 3 -12x - 24 Subtract -12x - (-12x), that gives 0 so we don't write anything under that. then +3 minus -24 is really +3+24 or 27, so the remainder is 27: -2x² + 5x - 12 x + 2)-2x³ + x² - 2x + 3 -2x³ - 4x² 5x² - 2x 5x² + 10x -12x + 3 -12x - 24 27 That's it. To write the answer we use -2x² + 5x - 12 + Edwin
