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Q. / divide by
- Set up synthetic division: To divide the function by , we can use synthetic division or long division. Let's use synthetic division.Set up the synthetic division by writing the coefficients of the polynomial: , (for all missing powers of down to ), , (for all missing powers of down to ), , (for all missing powers of down to ), , (for all missing powers of down to ), , (for all missing powers of down to ), .Place the zero of the divisor , which is , to the left of the synthetic division setup.
- Perform synthetic division: Start the synthetic division process by bringing down the leading coefficient, which is . Multiply this leading coefficient by the zero of the divisor () and write the result under the next coefficient. Add the numbers in the second column to get the new coefficient. Repeat this process for all coefficients.
- Complete synthetic division: Continue the synthetic division until you reach the last coefficient. The result of the synthetic division will give the coefficients of the quotient polynomial.
- Write quotient polynomial: Write down the quotient polynomial using the coefficients obtained from the synthetic division.The powers of in the quotient polynomial will start from and decrease by with each term.
- Check division result: Check the result by multiplying the quotient polynomial by the divisor and adding the remainder, if any.If the original polynomial is obtained, then the division was performed correctly.
