Answer :
Final answer:
To divide the given expression by the given polynomial using long division, follow these steps: divide the highest degree term, subtract the product from the original expression, and repeat until no higher degree terms are left. The final quotient is -3x²+9x-1.
Explanation:
To divide the expression -3x⁵-22x⁴-13x³+39x²+14x -6 by x³ +6x²-3x -5, we will use long division. Here are the steps:
Start with the highest degree term in the expression being divided, which is -3x⁵. Divide it by the highest degree term in the divisor, x³. The result is -3x².
Multiply the divisor (x³ +6x²-3x -5) by the result from step 1 (-3x²) and subtract the product from the original expression.
Repeat steps 1 and 2 with the new expression obtained from step 2.
Continue these steps until no higher degree terms are left in the new expression.
The final quotient is -3x²+9x-1.
