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SubjectsMathematics
बहुपद की घात
In Class 9 Mathematics, under Introduction to Polynomials, Degree of a Polynomial explains how to identify the highest exponent of a variable with a non-zero coefficient in a polynomial. Students learn to determine polynomial degree, distinguish constant, linear, quadratic and cubic polynomials, and understand why the zero polynomial has an undefined degree.
Correct answer: A. 2
Explanation: The degree of a polynomial is the highest exponent of its variable with a non-zero coefficient. The terms are 14x^2, -5x, and 1, and the greatest exponent of x is 2. Hence, its degree is 2. The term -5x has exponent 1, so 1 is not correct. Exam tip: Look at the highest power of the variable, not at the coefficients.
Correct answer: B. 0
Explanation: (-31) is a non-zero constant polynomial because it contains no variable. The degree of every non-zero constant polynomial is 0. It cannot be 1 because there is no term with a variable raised to the first power. Exam tip: Any non-zero constant such as 5, -12, or 3/4 has degree 0 when considered as a polynomial.
Correct answer: C. 3
Explanation: The coefficient of \(0x^6\) is zero, so it does not count as a term of the polynomial. The remaining polynomial is \(7x^3-4\), whose highest power of \(x\) is \(3\). Hence, its degree is \(3\). Option \(6\) is a close distractor, but the power of a zero-coefficient term cannot determine the degree. Exam tip: remove all zero-coefficient terms before finding the degree.
Correct answer: C. 10
Explanation: The degree of a polynomial is the greatest exponent of the variable among its terms. Here, the exponents are 10, 4, and 1, and the greatest is 10. Therefore, the correct answer is 10. The number 4 is only the exponent in the term 2x^4, not the degree of the entire polynomial. Exam tip: simplify the polynomial first, then identify the highest power of the variable.
Correct answer: A. 6
Explanation: The degree of a polynomial is the highest exponent of the variable with a non-zero coefficient. The exponents of the terms in the given polynomial are 0, 6, and 2. Since 6 is the greatest exponent, its degree is 6. The number 2 is only the exponent in the term \(-x^2\), not the degree of the whole polynomial. Exam tip: Look for the highest power of the variable, regardless of the order of terms.
Correct answer: B. 2
Explanation: On simplification, the like terms cancel: \(4x^4-4x^4=0\). Thus, the polynomial becomes \(6x^2-1\). The highest power of \(x\) with a non-zero coefficient is \(2\), so its degree is \(2\). Option 4 is incorrect because the \(x^4\) terms cancel completely. Exam tip: simplify a polynomial first, then identify the highest remaining exponent with a non-zero coefficient.
Correct answer: C. 9
Explanation: The degree of a polynomial is the highest exponent of the variable with a non-zero coefficient. Here, the powers of x are 9, 6, 2, and 0. The greatest power is 9, so the degree of the polynomial is 9. The number 13 is only the coefficient of x^9, not the degree. Exam tip: To find degree, look for the highest power of the variable, not the largest coefficient.
Correct answer: B. \(x^2+4x+1\)
Explanation: A quadratic polynomial has highest exponent 2. In \(x^2+4x+1\), the greatest power of \(x\) is 2, so it is quadratic. \(2x^3-x\) is cubic. Exam tip: identify the highest exponent first.
Correct answer: C. 4
Explanation: The degree of a polynomial is the highest power of the variable having a non-zero coefficient. Here, 0x^3 and 0x^2 are zero terms, so they do not affect the degree. In 3x^4, the power of x is 4; therefore, the degree is 4. The constant term 8 has degree 0. Exam tip: Ignore terms with zero coefficients before identifying the highest power.
Correct answer: B. 5
Explanation: Combining like terms gives \(x^5+x^5=2x^5\), so the simplified polynomial is \(2x^5+x^2\). The highest power of \(x\) is 5; therefore, its degree is 5. Adding the coefficients of \(x^5\) does not make the exponent 10. Exam tip: First simplify like terms, then identify the highest exponent to find the degree.
Correct answer: C. 1
Explanation: In the given expression, the coefficients of 0x^4 and 0x^2 are zero, so these terms do not contribute to the polynomial. The remaining polynomial is 11x-6, where the highest power of x is 1. Therefore, its degree is 1. Choosing 4 would be incorrect because the coefficient of x^4 is zero. Exam tip: Remove all terms with zero coefficients before finding the degree.
Correct answer: C. 7
Explanation: The degree of a polynomial is the greatest exponent of the variable in any of its terms. In the given polynomial, the powers of x are 2, 7, 3, and 0; the greatest is 7, so its degree is 7. Here, 12 is a coefficient, not an exponent, so it is not the degree. Exam tip: Writing terms in descending powers makes it easier to identify the degree.
Correct answer: B. 11
Explanation: The degree of a polynomial is the greatest exponent of its variable with a non-zero coefficient. Here, the exponents of x are 11 and 4, while 5 is a constant term. The greatest exponent is 11, so the degree is 11. Option 15 is the sum of exponents, not the degree. Exam tip: do not add exponents of separate terms; identify the highest exponent.
Correct answer: C. From the highest power 3 of x
Explanation: The degree of a polynomial is the highest power of its variable having a non-zero coefficient. Here, the powers of x are 3, 2, 1, and 0, so the highest power is 3 and the polynomial has degree 3. The number 8 is only a coefficient, not the degree. Exam tip: To find the degree, look for the term with the greatest exponent of the variable.
Correct answer: B. 1
Explanation: Combining like terms gives \(5x^2-5x^2=0\). Therefore, the simplified polynomial is \(6x-3\). The highest power of \(x\) is 1, so its degree is 1. Option 2 may seem tempting from the original expression, but the \(x^2\) terms cancel out. Exam tip: Always simplify a polynomial before finding its degree.
Correct answer: A. 8
Explanation: The degree of a polynomial is the greatest exponent of the variable in any term with a non-zero coefficient. Here, the exponents of x are 8, 5, 2, and 0. The greatest exponent is 8, so the degree of the polynomial is 8. Although 5 is the exponent in the second term, it is not the degree of the whole polynomial. Exam tip: Treat the constant term as having exponent 0, then identify the greatest exponent.
Correct answer: C. 2
Explanation: Here, \(x^0=1\), so the polynomial becomes \(1+9x^2-4=9x^2-3\). The highest exponent of \(x\) with a non-zero coefficient is \(2\), so its degree is \(2\). Note that \(9\) is a coefficient, not an exponent. Exam tip: simplify constant terms first, then identify the highest power of \(x\).
Correct answer: B. 6
Explanation: A term with coefficient 0 is a zero term, so it is not considered while finding the degree of a polynomial. Here, 0x^8 is a zero term; the remaining terms are 15x^6 and -4. The highest power of x among these terms is 6, so the degree is 6. Option 8 is a close distractor, but 0x^8 must not be counted. Exam tip: First remove all terms with zero coefficients before identifying the highest exponent.
Correct answer: D. 5
Explanation: The degree of a polynomial is the highest power of the variable with a non-zero coefficient. In the given polynomial, the powers of x are 1, 2, 3, and 5; the highest is 5. Therefore, its degree is 5. Option 3 is only the power of x^3, but the term x^5 is also present. Exam tip: Look for the greatest exponent of the variable, regardless of the order of terms.
Correct answer: A. \(3x^6-2x^2+1\)
Explanation: The degree of a polynomial is the highest power of the variable with a non-zero coefficient. In \(3x^6-2x^2+1\), the highest power of \(x\) is \(6\), so its degree is \(6\). In option B, the highest power is \(5\), so it is not correct. Exam tip: To find the degree, identify the term with the greatest exponent of the variable.
Correct answer: B. 4
Explanation: The degree of a polynomial is the greatest exponent of the variable in any term with a non-zero coefficient. Here, the exponents of the terms are 4, 2, and 0, so the greatest exponent is 4. The negative sign in the coefficient of
y does not affect the degree. Exam tip: First write the polynomial in simplified form, then identify the highest power of the variable.
Correct answer: C. 7
Explanation: The degree of a polynomial is the greatest exponent of the variable among its terms. In the given polynomial, the exponents of x are 2, 7, and 4; the greatest is 7. Therefore, the degree is 7. Note that 5 is the coefficient of x^7, not the degree. Exam tip: compare the exponents of the variable, not the coefficients.
Correct answer: C. 9
Explanation: The degree of a polynomial is the greatest exponent of its variable with a non-zero coefficient. Since the highest power given is 9, its degree is 9. Degree 0 applies to a non-zero constant polynomial, not to this case. Exam tip: find the highest power of the variable to determine the degree.
Correct answer: C. 3
Explanation: Combining like terms gives 2x^3+9x^3=11x^3. Thus, the simplified polynomial is 11x^3-4x+1. The highest power of x is 3, so its degree is 3. Here, 11 is a coefficient, not the degree. Exam tip: First simplify the polynomial, then identify the highest exponent of the variable with a non-zero coefficient.
Correct answer: C. 5
Explanation: The degree of a polynomial is the greatest exponent of the variable with a non-zero coefficient. In the given polynomial, the exponents of x are 2, 0, and 5. The greatest exponent is 5, so its degree is 5. Option 2 is not correct because it is only the degree of the term 4x^2. Exam tip: Arrange the polynomial in descending powers and identify the highest exponent to find its degree quickly.
