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Mathematics

Degree of a Polynomial

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.

Practice questions

If (F(x)=4x^{10}-4x^{10}+5x^6-5x^6+7x^3-2), what is the degree of (F(x))?If (S(x)=(x^5+3x^2)^2-x^{10}-6x^7+4x^4), what is the degree of (S(x))?For which value will ((w-9)x^{12}+(w^2-81)x^8+6x^4-5) have degree (4)?If the degree of (p(x)=(a^2-4)x^{11}+(a-2)x^7+5x^3-1) is (3), which value of (a) is correct?After simplifying (x^4(x^5-3x)-x^9+6x^6-2), what is the degree?If (q(x)=(k-1)^2x^{10}+(k^2-1)x^6+4x^2) and (k=1), what is the degree of (q(x))?A student says that the degree of the polynomial \(7-4x^3+x^6-2x^8\) is 6 because the term containing \(x^6\) is written in the middle. What is the student's error?If (f(x)=4x^8-9x^8+5x^8-3x^4+10), what is the degree of (f(x))?What is the total degree of (7x^5y^4-2x^3y^7+6xy^2-11)?With respect to (x), what is the degree of (5x^8y^3-4x^6y^9+7y^5-2)?Which of the following is a polynomial in two variables with total degree 5?If the degree of (2x^n+9x^{12}-4) is (n) and (n>12), which value of (n) is possible?If the degree of (6x^m+3x^9+5) is (9) and (m<9), which value of (m) is possible?A student says that the polynomial \(P(x)=(x^4-3x^2+1)-(x^4+2x^2-5)\) has degree 4 because an \(x^4\) term is visible. What is the correct evaluation of the student's claim?Which of the following statements about the degree of polynomials is correct?If (b\neq-4), what will be the degree of ((b+4)x^{14}+8x^5-1)?If (b=-4), what will be the degree of ((b+4)x^{14}+8x^5-1)?If \(p(x)\) and \(q(x)\) are non-zero polynomials, which statement about their degrees is always true?After simplifying (5x^7(x^2-1)-5x^9+2x^6), what is the degree?What is the degree of (0x^{15}+0x^{12}+0x^4-41)?