Question

Which facts did you include in your answer? Check all of the boxes that apply. Option 1: If there is no remainder, then the dividend is equal to the quotient times the divisor.

Option 2: The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.
Option 3: If there is a remainder, then it gets added on to the product of the quotient and the divisor.
Option 4: The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.

Answer 1

The fundamental facts to include regarding multiplication and division in mathematics are that the dividend is the product of the quotient and the divisor or this product plus the remainder, and that both the quotient and divisor are polynomials leading to a polynomial dividend.

Step-by-step explanation:

When dealing with division and multiplication in mathematics, several important facts are considered:

• Option 1: If there is no remainder, then the dividend is equal to the quotient times the divisor.
• Option 2: The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.
• Option 3: If there is a remainder, then it gets added on to the product of the quotient and the divisor.
• Option 4: The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.

These concepts are fundamental in understanding how to maintain balance in an equation during multiplication or division. It's important to remember that when multiplying or dividing terms within an equation, every part of the equation must be considered to ensure balance is maintained.