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← Back to Introduction to Polynomials

Mathematics

Definition of a Polynomial

बहुपद की परिभाषा

In Class 9 Mathematics, under Introduction to Polynomials, Definition of a Polynomial explains expressions in which variables have only non-negative integer powers. Students learn to distinguish polynomials from expressions containing negative, fractional, or other invalid exponents, identify constant and zero polynomials, and recognise polynomials by their highest power and basic type.

Practice questions

If (q(x)=x^6+x^{\frac{3}{2}}+2), why is (q(x)) not a polynomial?When will ((u+2)x^4+(u+2)x+15) become a constant polynomial?In (6x^8-5x^6+3), what are the coefficients of (x^7), (x^5), and (x)?If (r=3), what will be the degree of ((r^2-9)x^7+(r-1)x^4+x^2)?What is obtained by simplifying (x^3(x^2-5)-x^5+9x^3)?What type of polynomial is the simplified form (4x^3)?Which conclusion is correct for \(x^0+\sqrt{2}x^5-\frac{4x^2}{9}\)?If (d=-1), what will be the degree of ((d+1)x^5+(2d+3)x^2+7)?For which value will the degree of ((2a-8)x^6+(a+1)x^3+4) be (3)?Why is (\frac{x^2-4}{x-2}) not considered a polynomial in its original form?What type of polynomial is the simplified form (x+2)?Which of the following expressions is not a polynomial in x?Which option is a polynomial and all its non-zero variable terms have even powers?When will ((w^2-1)x^4+(w-1)x^2+6) become a constant polynomial?If (z=-2), what will be the degree of ((z+2)x^5+(z^2-4)x^3+9x-1)?Which expression is not a polynomial because the variable appears as an exponent?Which expression is a polynomial in (x) and has degree (0)?In (x^4-4x^2+4), what are the coefficients of (x^3) and (x) respectively?Which option correctly identifies a polynomial with missing powers?If (p(x)=(a-5)x^6+4x^2-9) is to be exactly a quadratic polynomial, what is the value of (a)?