Question

Use long division to find the quotient below:

(5x ^5 −90x^ 2 −135x)÷(x−3)
a) 5x^4 15x^3 - 45x^2 - 45x b) 5x^4 - 5x^3 25x^2 - 45x
c) 5x^4 5x^3 - 25x^2 - 45x
d) 5x^4 - 15x^3 45x^2 - 45x

Answer 1

To divide the polynomial (5x^5 − 90x^2 − 135x) by (x − 3) using long division, follow these steps: Divide, write, multiply, subtract, repeat, and obtain the final quotient as 5x^4 - 15x^3 45x^2 - 45x.

Step-by-step explanation:

To divide the polynomial (5x^5 − 90x^2 − 135x) by (x − 3) using long division, follow these steps:

1. Divide the first term of the numerator (5x^5) by the first term of the denominator (x).
2. Write the quotient (5x^4) above the line.
3. Multiply the denominator (x − 3) by the quotient (5x^4) and write the result (5x^5 − 15x^4) below the line.
4. Subtract the result from the numerator (5x^5 − 90x^2 − 135x) and bring down the next term.
5. Repeat steps 1-4 until all terms of the numerator have been used.
6. The final quotient is the terms written above the line: 5x^4 - 15x^3.

Therefore, the correct answer is option d) 5x^4 - 15x^3 45x^2 - 45x.