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10 Questions

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Polynomial Division and Factorization

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Questions and Answers

What method can be used to divide a polynomial by a monomial?

Dividing each term of the polynomial by the monomial (correct)

Expanding both the polynomial and the monomial

Multiplying each term of the polynomial by the monomial

Factoring both the polynomial and the monomial

What is the relation between Dividend, Divisor, Quotient, and Remainder in general?

Dividend = Divisor × Quotient

Dividend = Divisor × Quotient + Remainder (correct)

Dividend = Divisor + Quotient

Dividend = Divisor - Quotient + Remainder

What is the inverse operation of multiplication when dealing with numbers?

Subtraction

Division (correct)

Exponentiation

Addition

How should factors a and b be chosen when dealing with a polynomial's coefficients?

$a + b$ should equal the coefficient of x Signup and view all the answers

What is the recommended method for dividing a polynomial by a polynomial?

Factoring both the dividend and divisor polynomials Signup and view all the answers

What happens when dividing algebraic expressions where the remainder is not zero?

$\text{Dividend} = \text{Divisor} \times \text{Quotient} - \text{Remainder}$ Signup and view all the answers

In division of algebraic expressions, what does the term 'common factor method' refer to?

Factoring out common factors before division Signup and view all the answers

What is necessary to do in order to proceed with division by polynomials?

Factorize both polynomials. Signup and view all the answers

Why can't we proceed by dividing each term in the dividend polynomial by the divisor polynomial when dealing with division of polynomials?

It leads to wrong results due to incorrect division process. Signup and view all the answers

When dividing a polynomial by a monomial, what will be obtained if each term of the dividend is divided by the monomial?

The quotient of that particular term only. Signup and view all the answers