The degree of 3x^4 + x^3 + 5 is decided by which term?
Answer and explanation
Correct answer: 3x^4
The degree of a polynomial is determined by the term containing the highest power of the variable, provided its coefficient is non-zero. In 3x^4 + x^3 + 5, the powers of x are 4, 3 and 0 respectively. The term 3x^4 contains the greatest power, x^4, so it determines the degree of the polynomial, which is 4. The coefficient 3 does not itself determine the degree; it only multiplies x^4. Similarly, x^3 has a lower power and 5 is a constant term. Therefore option A is the correct term.
Frequently asked questions
What is the correct answer to this question?
3x^4
Why is this the correct answer?
The degree of a polynomial is determined by the term containing the highest power of the variable, provided its coefficient is non-zero. In 3x^4 + x^3 + 5, the powers of x are 4, 3 and 0 respectively. The term 3x^4 contains the greatest power, x^4, so it determines the degree of the polynomial, which is 4. The coefficient 3 does not itself determine the degree; it only multiplies x^4. Similarly, x^3 has a lower power and 5 is a constant term. Therefore option A is the correct term.
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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