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Write POLYNOMIAL if the algebraic expression is Polynomial, write NOT A POLYNOMIAL if not. 1. 4x - 7 2. x² - 3x + 4 3. 2/x + 5x³ + 2x 4. 1/3 x² - 1/4 x + 6 5. √3 y² - 2y - 3

Answer :

Final answer:

The expressions 1. 4x - 7, 2. x² - 3x + 4, 4. 1/3 x² - 1/4 x + 6 and 5. √3 y² - 2y - 3 are Polynomials. However, expression 3. 2/x + 5x³ + 2x is Not a Polynomial because it involves division by a variable.

Explanation:

A polynomial is an algebraic expression consisting of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Let's verify one by one:

  1. 4x - 7: This is a Polynomial. It contains variables with positive integer exponents and involves operation of addition and subtraction.
  2. x² - 3x + 4: This is a Polynomial. It is a quadratic polynomial, variables have positive integer exponents.
  3. 2/x + 5x³ + 2x: This is Not a Polynomial. It involves a division operation by a variable which is not allowed in defining a polynomial.
  4. 1/3 x² - 1/4 x + 6: This is a Polynomial. It is a quadratic polynomial with variables having positive integer exponents.
  5. √3 y² - 2y - 3: This is a Polynomial. The square root is not applied on the variable, rather the constant, therefore this expression can still be considered a polynomial.

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