# SOLUTION: Divide using long division: 6x^3 + 19x^2 + x - 10 / 2x - 1

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Divide using long division: 6x^3 + 19x^2 + x - 10 / 2x - 1      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Rational Functions, analyzing and graphing Solvers Lessons Answers archive Quiz In Depth

 Question 148086: Divide using long division: 6x^3 + 19x^2 + x - 10 / 2x - 1Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website! ``` Start with this: ---------------------- 2x - 1 )6x³ + 19x² + x - 10 2x divides into 6x³ to give 3x² Put that at the top, above the 19x² 3x² ---------------------- 2x - 1 )6x³ + 19x² + x - 10 Multiply the 3x² by the 2x - 1 to get 6x³ - 3x², so write that at the bottom and draw a line: 3x² ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- Now subtract, by mentally changing the signs on the bottom row. We get 22x², so we write that at the bottom, and bring down the next term x: 3x² ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x 2x divides into 22x² to give 11x Put that at the top above the x 3x² + 11x ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x Multiply the 11x by the 2x - 1 to get 22x² - 11x, so write that at the bottom and draw a line: 3x² + 11x + 6 ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x 22x² - 11x ---------- Now subtract, by mentally changing the signs on the bottom row. We get 12x, so we write that at the bottom, and bring down the next term -10: 3x² + 11x ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x 22x² - 11x ---------- 12x - 10 2x divides into 12x to give 6 Put that at the top above the -10 3x² + 11x + 6 ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x 22x² - 11x ---------- 12x - 10 Multiply the 6 by the 2x - 1 to get 12x - 6, so write that at the bottom and draw a line: 3x² + 11x + 6 ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x 22x² - 11x ---------- 12x - 10 12x - 6 -------- Now subtract, by mentally changing the signs on the bottom row. We get -4, so we write that at the bottom, and we're finished because there are no more terms to bring down: 3x² + 11x + 6 ---------------------- 2x - 1 )6x³ + 19x² + x - 10 6x³ - 3x² ---------- 22x² + x 22x² - 11x ---------- 12x - 10 12x - 6 -------- - 4 Now we write the answer using or if you like: Edwin```