Classify the following as a constant, linear, quadratic and cubic polynomials
(i) $2-x^{2}+x^{3}$
(ii) $3 x^{3}$
(iii) $5 t-\sqrt{7}$
(iv) $4-5 y^{2}$
(v) 3
(vi) $2+x$
(vii) $y^{3}-y$
(viii) $1+x+x^{2}$
(ix) $t^{2}$
(x) $\sqrt{2} x-1$
Thinking Process
(i) Firstly check the maximum exponent of the variable..
(ii) If the maximum exponent of a variable is 0 , then it is a constant polynomial.
(iii) If the maximum exponent of a variable is 1 , then it is a linear polynomial.
(iv) If the maximum exponent of a variable is 2 , then it is a quadratic polynomial.
(v) If the maximum exponent of a variable is 3 , then it is a cubic polynomial.
(i) Polynomial 2 – x2 + x3 is a cubic polynomial, because maximum exponent of x is 3.
(ii) Polynomial 3x3 is a cublic polynomial, because maximum exponent of x is 3.
(iii) Polynomial 5t -√7 is a linear polynomial, because maximum exponent of t is 1.
(iv) Polynomial 4- 5y2 is a quadratic polynomial, because maximum exponent of y is 2.
(v) Polynomial 3 is a constant polynomial, because the exponent of variable is 0. ’
(vi) Polynomial 2 + x is a linear polynomial, because maximum exponent of x is 1.
(vii) Polynomial y3 – y is a cubic polynomial, because maximum exponent of y is 3.
(viii) Polynomial 1 + x+ x2 is a quadratic polynomial, because maximum exponent of xis 2.
(ix) Polynomial t2 is a quadratic polynomial, because maximum exponent of t is 2.
(x) Polynomial √2x-1 is a linear polynomial, because maximum exponent of xis 1.
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