The degree of 3x⁴ + 7x² − 5 is decided by which term?
Answer and explanation
Correct answer: 3x⁴
The governing concept is the degree of a polynomial. For a non-zero polynomial, the degree is the greatest exponent of the variable among terms with non-zero coefficients. In 3x⁴ + 7x² − 5, the exponents of x are 4, 2 and 0. Since 4 is the greatest exponent, the term containing it is 3x⁴, so option A is correct. The coefficient 3 affects the value of the term but does not change its degree. The term 7x² has degree 2, the constant term −5 has degree 0, and 7 by itself is not a complete term appearing in the polynomial. Consequently, neither the largest coefficient nor the constant term determines the degree; the highest power of x does.
Frequently asked questions
What is the correct answer to this question?
3x⁴
Why is this the correct answer?
The governing concept is the degree of a polynomial. For a non-zero polynomial, the degree is the greatest exponent of the variable among terms with non-zero coefficients. In 3x⁴ + 7x² − 5, the exponents of x are 4, 2 and 0. Since 4 is the greatest exponent, the term containing it is 3x⁴, so option A is correct. The coefficient 3 affects the value of the term but does not change its degree. The term 7x² has degree 2, the constant term −5 has degree 0, and 7 by itself is not a complete term appearing in the polynomial. Consequently, neither the largest coefficient nor the constant term determines the degree; the highest power of x does.
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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