polynomial long division (6x³- 16x²+ 17x-6) ÷ (3x-2)
Answer (1)
Answer:Step-by-step explanation:Think of it like regular long division, but with variables instead of just numbers.You start by asking yourself:“What do I multiply 3x by to get 6x³?”The answer is 2x². So you write 2x² at the top of your answer.Then, you multiply 2x² by the whole divisor (3x - 2), which gives you:6x³ - 4x²Now, subtract that from the original expression:(6x³ - 16x²) minus (6x³ - 4x²) leaves you with -12x².Then you bring down the next term, which is +17x.Now you’re working with -12x² + 17x.Next, you ask:“What do I multiply 3x by to get -12x²?”That’s -4x. Add that to your answer on top.Multiply -4x by (3x - 2), and you get -12x² + 8x.Subtract again:(-12x² + 17x) minus (-12x² + 8x) gives you 9x.Bring down the next term: -6. Now you’re working with 9x - 6.Ask again:“What do I multiply 3x by to get 9x?”That’s 3. Add it to your answer.Multiply 3 by (3x - 2), and you get 9x - 6.Subtract one last time:(9x - 6) minus (9x - 6) gives you 0 — no remainder!
