QQuestionMathematics
QuestionMathematics
Which of the following is a polynomial?
A. x- 2 - 1
B. 1 /x + 2
C. (x^6 – 4)/(x- 6 + 1)
D. x^4 - 2
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Answer
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Step 1: Recall the definition of a polynomial.
A polynomial is an expression consisting of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents.
Step 2: Examine the given options.
A. x - 2 - 1 This is a difference between two terms, x and - 2 - 1. Both terms are polynomials since they involve only addition, subtraction, and multiplication. Thus, option A is a polynomial. B. 1 /x + 2 This expression contains a term with a variable in the denominator, 1 /x. Since polynomials cannot have negative integer exponents or variables in the denominator, option B is not a polynomial. C. (x^6 – 4)/(x - 6 + 1) This expression is a fraction with two polynomials in the numerator and denominator. The numerator, x^6 – 4, is a polynomial, but the denominator, x - 6 + 1, is not a polynomial because of the addition in the denominator. Thus, option C is not a polynomial. D. x^4 - 2 This is a difference between two terms, x^4 and - 2. Both terms are polynomials since they involve only addition, subtraction, and multiplication. Thus, option D is a polynomial.
Final Answer
The polynomials are options A and D, which are x - 2 - 1 and x^4 - 2.
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