Expand by using binomial and find the degree of polynomial (x+√x3-1)5+(x-√x3-1)5 is

Question

Expand by using binomial and find the degree of polynomial (x+√x3-1)5+(x-√x3-1)5 is (A) 7 (B) 6 (C) 5 (D) 4

Tardigrade Admin · Accepted Answer

(x+√x3-1)5+(x-√x3-1)5 =2[x5+ 5 C2 x3(x3-1)+ 5 C4 x(x3-1)2] =2[x5+10 x3(x3-1)+5 x4(x6-2 x3+1]. =10 x7+20 x6+2 x5-20 x4-20 x3+10 x ∴ polynomial has degree 7

Q. Expand by using binomial and find the degree of polynomial
$(x + x^{3} - 1)^{5} + (x - x^{3} - 1)^{5}$ is

7

6

5

4

$(x + x^{3} - 1)^{5} + (x - x^{3} - 1)^{5}$
$= 2 [x^{5} +^{5} C_{2} x^{3} (x^{3} - 1) +^{5} C_{4} x (x^{3} - 1)^{2}]$
$= 2 [x^{5} + 10 x^{3} (x^{3} - 1) + 5 x^{4} (x^{6} - 2 x^{3} + 1]$
$= 10 x^{7} + 20 x^{6} + 2 x^{5} - 20 x^{4} - 20 x^{3} + 10 x$
$∴$ polynomial has degree $7$

Q. Expand by using binomial and find the degree of polynomial (x+x3−1​)5+(x−x3−1​)5 is

7

6

5

4

(x+x3−1​)5+(x−x3−1​)5 =2[x5+5C2​x3(x3−1)+5C4​x(x3−1)2] =2[x5+10x3(x3−1)+5x4(x6−2x3+1] =10x7+20x6+2x5−20x4−20x3+10x ∴ polynomial has degree 7

Q. Expand by using binomial and find the degree of polynomial
$(x + x^{3} - 1)^{5} + (x - x^{3} - 1)^{5}$ is

$(x + x^{3} - 1)^{5} + (x - x^{3} - 1)^{5}$
$= 2 [x^{5} +^{5} C_{2} x^{3} (x^{3} - 1) +^{5} C_{4} x (x^{3} - 1)^{2}]$
$= 2 [x^{5} + 10 x^{3} (x^{3} - 1) + 5 x^{4} (x^{6} - 2 x^{3} + 1]$
$= 10 x^{7} + 20 x^{6} + 2 x^{5} - 20 x^{4} - 20 x^{3} + 10 x$
$∴$ polynomial has degree $7$