Chek wheather y-1 is a factor y^20-1
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Answer:
Yes
Note:
★ The possible values of the variable for which the polynomial becomes zero are called its zeros .
★ If (x - a) is a factor of a polynomial p(x)., then x = a is its zero and hence p(a) = 0 .
Solution:
Here ,
The given polynomial is ;
y^20 - 1 .
We need to check whether (y - 1) is a factor of y^20 - 1 or not .
Thus,
Let the given polynomial be p(y) .
Thus,
p(y) = y^20 - 1
Also ,
If y - 1 = 0 , then
y = 1
Now,
=> p(y) = y^20 - 1
=> p(1) = 1^20 - 1
=> p(1) = 1 - 1
=> p(1) = 0
Since , p(1) = 0 thus y = 1 is a zero of the given polynomial p(y) and hence (y - 1) is a factor of the given polynomial p(y) = y^20 - 1 .
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