In Exercises 27 - 46, use synthetic division to divide. $\frac{x^5-13x^4-120x+80}{x+3}$

Step by Step Solution: Step 1. Write the coefficients of the polynomial in standard form Step 2. Set up the synthetic division tableau, write the negation of the divisor in the top row and the coefficients of the polynomial in the second row Step 3. Draw a vertical line to separate the coefficient row from the working row Step 4. Bring down the first coefficient without change Step 5. Multiply the number just brought down by the negation of the divisor and write the result below the next coefficient Step 6. Add the two numbers in the bottom row, write the sum below the line Step 7. Repeat steps 5 and 6 until all coefficients are included in the tableau Step 8. The terms in the bottom row of the tableau are the coefficients of the quotient polynomial, the remainder is the number to the right of the vertical line Step 9. Write the quotient polynomial Step 10. Write the remainder and the divisor in the original division format, using fractional or mixed number format as appropriate Final Answer: The quotient polynomial is $x^4-16x^3+48x^2-144x+432$ and the remainder is -1296. Thus, $x^5-13x^4-120x+80=(x+3)(x^4-16x^3+48x^2-144x+432)-1296$