Question

The expression $(x+(x^3-1{)}^{\frac{1}{2}}{)}^5+(x-(x^3-1{)}^{\frac{1}{2}}{)}^5$ is a polynomial of a degree :

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

Let ${(x}^3-{1)}^{\frac{1}{2}}=a$

$\therefore {(x+a)}^5+{(x-a)}^5$.

$=2[{{}^{5}C}_o{x}^5{{+}^{5}C}_2{x}^3{a}^2+{{}^{5}C}_{1}x{a}^4]$

$=2[x^5{{+}^{5}C}_2{x}^3{.(x}^3-1)+5.x.{(x^3-1)}^2]$

$\therefore$ Degree of polynomial $=7.$

Hence the answer is $7.$