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InterviewSolution
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Classify the following as a constant, linear, quadratic and cubic polynomials:(i) 2 – x2 + x3(ii) 3x3(iii) 5t – √7(iv) 4 – 5y2(v) 3(vi) 2 + x(vii) y3 – y(viii) 1 + x + x2(ix) t2 (x) √2x – 1 |
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Answer» Constant polynomials: The polynomial of the degree zero. Linear polynomials: The polynomial of degree one. Quadratic polynomials: The polynomial of degree two. Cubic polynomials: The polynomial of degree three. (i) 2 – x2 + x3 Powers of x = 2, and 3 respectively. Highest power of the variable x in the given expression = 3 Hence, degree of the polynomial = 3 Since it is a polynomial of the degree 3, it is a cubic polynomial. (ii) 3x3 Power of x = 3. Highest power of the variable x in the given expression = 3 Hence, degree of the polynomial = 3 Since it is a polynomial of the degree 3, it is a cubic polynomial. (iii) 5t – √7 Power of t = 1. Highest power of the variable t in the given expression = 1 Hence, degree of the polynomial = 1 Since it is a polynomial of the degree 1, it is a linear polynomial. (iv) 4 – 5y2 Power of y = 2. Highest power of the variable y in the given expression = 2 Hence, degree of the polynomial = 2 Since it is a polynomial of the degree 2, it is a quadratic polynomial. (v) 3 There is no variable in the given expression. Let us assume that x is the variable in the given expression. 3 can be written as 3x0. i.e., 3 = x0 Power of x = 0. Highest power of the variable x in the given expression = 0 Hence, degree of the polynomial = 0 Since it is a polynomial of the degree 0, it is a constant polynomial. (vi) 2 + x Power of x = 1. Highest power of the variable x in the given expression = 1 Hence, degree of the polynomial = 1 Since it is a polynomial of the degree 1, it is a linear polynomial. (vii) y3 – y Powers of y = 3 and 1, respectively. Highest power of the variable x in the given expression = 3 Hence, degree of the polynomial = 3 Since it is a polynomial of the degree 3, it is a cubic polynomial. (viii) 1 + x + x2 Powers of x = 1 and 2, respectively. Highest power of the variable x in the given expression = 2 Hence, degree of the polynomial = 2 Since it is a polynomial of the degree 2, it is a quadratic polynomial. (ix) t2 Power of t = 2. Highest power of the variable t in the given expression = 2 Hence, degree of the polynomial = 2 Since it is a polynomial of the degree 2, it is a quadratic polynomial. (x) √2x – 1 Power of x = 1. Highest power of the variable x in the given expression = 1 Hence, degree of the polynomial = 1 Since it is a polynomial of the degree 1, it is a linear polynomial. |
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