Which of the following expressions are polynomials? In case of a polyn

1.	Which of the following expressions are polynomials? In case of a polynomial, write its degree. (i) x5−2x3+x+√3 (ii) y3+√3y (iii) t2−25t+√5 (iv) x1000−1 (v) 1√2x2−√2x+2 (vi) x−2+2x−1+3 (vii) 1 (viii) −35 (ix) x22−2x2 (x) 2√2x2−8 (xi) 12x2 (xii) 1√5x12+1 (xiii) 35x2−73x+9 (xiv) x4−x32+x−3 (xv) 2x3+3x2+√x−1
Answer» Which of the following expressions are polynomials? In case of a polynomial, write its degree. (i) $x^{5} - 2 x^{3} + x + \sqrt{3}$ (ii) $y^{3} + \sqrt{3} y$ (iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$ (iv) $x^{1000} - 1$ (v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$ (vi) $x^{- 2} + 2 x^{- 1} + 3$ (vii) $1$ (viii) $\frac{- 3}{5}$ (ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$ (x) $\sqrt[2]{2} x^{2} - 8$ (xi) $\frac{1}{2 x^{2}}$ (xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$ (xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$ (xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$ (xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

Which of the following expressions are polynomials? In case of a polynomial, write its degree. (i) x5−2x3+x+√3 (ii) y3+√3y (iii) t2−25t+√5 (iv) x1000−1 (v) 1√2x2−√2x+2 (vi) x−2+2x−1+3 (vii) 1 (viii) −35 (ix) x22−2x2 (x) 2√2x2−8 (xi) 12x2 (xii) 1√5x12+1 (xiii) 35x2−73x+9 (xiv) x4−x32+x−3 (xv) 2x3+3x2+√x−1

Answer»

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$