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  • Classify the following as a constant, linear, quadratic and cubic polynomials: (i) 2-x^{2}+x^{3} (ii) x^{3} (iii) 5t-\sqrt{7} (iv) 4-5y^{2} (v)3.x^{0} (vi)2+x (vii) y^{3}-y (viii) 1+x+x^{2} (ix) t^{2} (x) \sqrt{2}x-1

Classify the following as a constant, linear, quadratic and cubic polynomials:

(i) 2-x^{2}+x^{3}

(ii) x^{3}

(iii) 5t-\sqrt{7}

(iv) 4-5y^{2}

(v)3.x^{0}

(vi)2+x

(vii) y^{3}-y

(viii) 1+x+x^{2}

(ix) t^{2}

(x) \sqrt{2}x-1

 

Answers (1)

(i) Cubic Polynomial

(ii) Cubic Polynomial

(iii) Linear Polynomial

(iv) Quadratic Polynomial

(v) Constant Polynomial

(vi) Linear Polynomial

(vii) Cubic Polynomial

(viii) Quadratic Polynomial

(ix) Quadratic Polynomial

(x) Linear Polynomial

Solution

Degree of a polynomial: Degree of a polynomial is the highest power of the polynomial’s monomials with non-zero coefficient

Depending on the degree we can classify functions as:

  • Constant – Degree is zero
  • Linear – Degree is one
  • Quadratic – Degree is two
  • Cubic – Degree is three

            (i) 2-x^{2}+x^{3}  

            Here highest power of x is three therefore degree is three.

            Cubic polynomial.

            (ii) x^{3}

            Here highest power of x is three therefore degree is three.

            Cubic polynomial.

            (iii) 5t-\sqrt{7}

            Here highest power of t is one therefore degree is one.

            Linear polynomial.

            (iv) 4-5y^{2}

            Here highest power of y is two therefore degree is two.

            Quadratic polynomial.

            (v) 3.x^{0}

            Here highest power of x is zero therefore degree is zero.

            Constant polynomial.

            (vi) 2+x

            Here highest power of x is one therefore degree is one.

            Linear polynomial.

           (vii) y^{3}-y

            Here highest power of y is three therefore degree is three.

            Cubic polynomial.

           (viii) 1+x+x^{2}

            Here highest power of x is two therefore degree is two.

            Quadratic polynomial.

            (ix) t^{2}

            Here highest power of t is two therefore degree is two.

            Quadratic polynomial.

             (x) \sqrt{2}x-1

            Here highest power of x is one therefore degree is one.

            Linear polynomial.

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