Question

Find 3x⁴ −16x³ −15x² 17x−2 /x−6?

a) 3x³+2x²−7x+5− 32/x−6
​b) 3x³−2x² +7x−5− 32/x−6
c) 3x³−2x²+7x−5+ 32/x−6
d) 3x³ +2x²−7x+5+32/ x−6

Answer 1

To find the quotient of the polynomial division, we use polynomial long division to divide 3x⁴ − 16x³ − 15x² + 17x − 2 by x − 6. We arrive at the quotient 3x³ + 2x² - 7x + 5 with a remainder of − 32, making a) the correct answer.

Step-by-step explanation:

The student's question involves finding the quotient when dividing the polynomial 3x⁴ − 16x³ − 15x² + 17x − 2 by x − 6. This process is known as polynomial long division. We'll divide the terms one at a time, subtracting off the obtained product at each step to find the remainder.

1. Divide 3x⁴ by x to get 3x³.
2. Multiply x − 6 by 3x³ and subtract it from the polynomial.
3. Bring down the next term and repeat the process until all terms have been divided.

Through this step-by-step process, we find that the quotient is 3x³ + 2x² - 7x + 5 and the remainder is − 32. Therefore the correct answer choice is a). 3x³ + 2x² - 7x + 5 − 32/(x− 6).