Final answer:
The quotient of 6x³−x²−11x−5 divided by x−1 is 6x²−5x−5, which is option (d). This is found using polynomial long division, where terms are divided individually . option d is correct answer.
Step-by-step explanation:
To find the quotient of 6x³−x²−11x−5 divided by x−1, we can use either polynomial long division or synthetic division, as both provide a method to divide polynomials. In this case, let's use polynomial long division to illustrate the process:
- Divide the first term of the numerator by the first term of the divisor. Here, 6x³ divided by x gives 6x². Write 6x² above the division bar.
- Multiply the entire divisor by 6x² and subtract the result from the numerator.
- The new polynomial under the division bar is −5x²−11x. Now, divide −5x² by x to get −5x and place this term above the division bar next to 6x².
- Repeat the multiplication and subtraction process.
- The next term is 5x, which when multiplied by the divisor and subtracted from the polynomial leaves a new polynomial.
- Finally, dividing −5x by x gives −5, which is placed above the division bar.
- Performing the last multiplication and subtraction, we find there's no remainder.
- Thus, the quotient is 6x²−5x−5, which corresponds to option (d)
When performing polynomial division, write each term neatly in the corresponding columns, aligning like terms, and ensure to subtract properly to find the correct quotient.