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?

<p>$a + b$ should equal the coefficient of x (A)</p> Signup and view all the answers

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

<p>Factoring both the dividend and divisor polynomials (D)</p> Signup and view all the answers

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

<p>$\text{Dividend} = \text{Divisor} \times \text{Quotient} - \text{Remainder}$ (A)</p> Signup and view all the answers

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

<p>Factoring out common factors before division (C)</p> Signup and view all the answers

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

<p>Factorize both polynomials. (A)</p> 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?

<p>It leads to wrong results due to incorrect division process. (B)</p> 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?

<p>The quotient of that particular term only. (D)</p> Signup and view all the answers

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