The degree of the polynomial 5x^6 + 2x^4 − 11 is determined by which term?
Answer and explanation
Correct answer: 5x⁶
The degree of a non-zero polynomial in one variable is the greatest exponent of the variable having a non-zero coefficient. In 5x^6 + 2x^4 − 11, the variable powers are 6, 4, and 0, because the constant term −11 can be viewed as −11x^0. The greatest power is 6, and it occurs in the term 5x^6. Therefore, option A is correct and the polynomial has degree 6. The coefficient 5 does not determine the degree; it only multiplies the term. The term 2x^4 has a smaller exponent, the constant −11 has degree 0, and the number 2 alone is not a term of the given polynomial.
Frequently asked questions
What is the correct answer to this question?
5x⁶
Why is this the correct answer?
The degree of a non-zero polynomial in one variable is the greatest exponent of the variable having a non-zero coefficient. In 5x^6 + 2x^4 − 11, the variable powers are 6, 4, and 0, because the constant term −11 can be viewed as −11x^0. The greatest power is 6, and it occurs in the term 5x^6. Therefore, option A is correct and the polynomial has degree 6. The coefficient 5 does not determine the degree; it only multiplies the term. The term 2x^4 has a smaller exponent, the constant −11 has degree 0, and the number 2 alone is not a term of the given polynomial.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Degree of a Polynomial.
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