Mastering Polynomial Long Division with Remainders

The video tutorial explains how to perform polynomial long division. It starts by matching the leading term and proceeds through several steps of division, subtraction, and bringing down terms. The process is repeated until the remainder is found, which is then expressed as a fraction. The final result of the division is presented as a polynomial with a fractional remainder.

What is the goal of polynomial long division?

• To find the roots of the polynomial

• To match the leading term

• To factorize the polynomial

• To simplify the polynomial

What should be multiplied by 2x squared to get 6x to the fourth?

• 2x

• 6x squared

• 3x

• 3x squared

What is the result of subtracting 6x to the fourth from 6x to the fourth?

• 6x squared

• 6x to the fourth

• 0

• 12x to the fourth

What should be multiplied by 2x squared to get negative 2x cubed?

• Negative 1

• Negative 2x squared

• Negative 2x

• Negative x

What is the result of subtracting negative 2x cubed from 2x cubed?

• Negative 4x cubed

• 2x cubed

• 0

• 4x cubed

What should be multiplied by 2x squared to get 6x squared?

• 3

• 2

• 6

• 3x

What is the result of subtracting 6x squared from 6x squared?

• 12x squared

• 0

• 6x squared

• Negative 6x squared

What is the remainder when dividing the given polynomials?

• 5

• 3

• Negative 3

• Negative 5

What is the final answer when dividing the given polynomials?

• 3x squared minus x minus 3 minus 5 over 2x squared minus 1

• 3x squared plus x minus 3 minus 5 over 2x squared minus 1

• 3x squared minus x plus 3 plus 5 over 2x squared minus 1

• 3x squared minus x plus 3 minus 5 over 2x squared minus 1