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Question:

Classify the following as linear, quadratic and cubic polynomials:(i) x² + x (ii) x - x³ (iii) y + y² + 4 (iv) 1 + x (v) 3t (vi) r² (vii) 7x³

Solution:

(i) The highest degree of x in x² + x is 2, so it is a quadratic polynomial. (ii) The highest degree of x in x - x³ is 3, so it is a cubic polynomial. (iii) The highest degree of y in y + y² + 4 is 2, so it is a quadratic polynomial. (iv) The highest degree of x in (1 + x) is 1, so it is a linear polynomial. (v) The highest degree of t in 3t is 1, so it is a linear polynomial. (vi) The highest degree of r in r² is 2, so it is a quadratic polynomial. (vii) The highest degree of x in 7x³ is 3, so it is a cubic polynomial.