Classify the following as a constant, linear,

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Question:

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.

Solution:

(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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