Dividend

Definition

In the context of dividing polynomials, the dividend is the polynomial that is being divided. It is the expression that is placed in the numerator of the division problem and represents the value that needs to be divided by the divisor.

5 Must Know Facts For Your Next Test

1. The degree of the dividend must be greater than or equal to the degree of the divisor for the division process to be possible.
2. The leading coefficient of the dividend must be a non-zero value for the division process to be possible.
3. The division of polynomials can be performed using the long division algorithm or the synthetic division algorithm.
4. The quotient and remainder obtained from dividing the dividend by the divisor must satisfy the equation: dividend = divisor × quotient + remainder.
5. The degree of the remainder, if it exists, must be less than the degree of the divisor.

Review Questions

• Explain the relationship between the dividend, divisor, quotient, and remainder in the context of dividing polynomials.
  • In the context of dividing polynomials, the dividend is the polynomial that is being divided, the divisor is the polynomial that is used to divide the dividend, the quotient is the result of the division operation, and the remainder is the value that is left over after the division. The dividend, divisor, quotient, and remainder must satisfy the equation: dividend = divisor × quotient + remainder. The degree of the remainder, if it exists, must be less than the degree of the divisor.
• Describe the conditions necessary for the division of polynomials to be possible.
  • For the division of polynomials to be possible, the degree of the dividend must be greater than or equal to the degree of the divisor, and the leading coefficient of the dividend must be a non-zero value. If these conditions are not met, the division process cannot be performed, and the division problem cannot be solved.
• Analyze the role of the dividend in the context of dividing polynomials and explain how it affects the overall division process.
  • The dividend plays a crucial role in the division of polynomials. As the expression that is being divided, the dividend determines the outcome of the division process. The degree and leading coefficient of the dividend directly impact the feasibility of the division, as well as the resulting quotient and remainder. The dividend must have a degree greater than or equal to the divisor, and a non-zero leading coefficient, for the division to be possible. Additionally, the dividend, divisor, quotient, and remainder must satisfy the equation: dividend = divisor × quotient + remainder, which highlights the central importance of the dividend in the overall division process.

Related terms

Divisor: The divisor is the polynomial that is used to divide the dividend. It is the expression that is placed in the denominator of the division problem and represents the value that the dividend is being divided by.

Quotient: The quotient is the result of dividing the dividend by the divisor. It represents the outcome of the division operation and is the polynomial that is placed in the answer.

Remainder: The remainder is the value that is left over after the dividend has been divided by the divisor. It represents the portion of the dividend that could not be evenly divided by the divisor.