Factor : y^{7} + y

aramutselv

aramutselv

Answered question

2021-12-11

Factor : y7+y

Answer & Explanation

Lynne Trussell

Lynne Trussell

Beginner2021-12-12Added 32 answers

Step 1
We have to find the factor of y7+y.
Factorization is the process of taking common from the given expressions, the terms which get common we can call it as factor of the expression.
Here,
y7+y
taking y common from y7(y6y) and y
y7+y=y6y+y
=y(y6+1)
Further we can rewrite:
y(y6+1)=y((y2)3+13)
Step 2
Now applying the formula a3+b3=(a+b)(a2ab+b2) for the expression ((y2)2+13)
Here a=y2,b=1
y7+y=y(y6+1)
=y((y2)3+13)
=y(y2+1)(y2y1+1)
=y(y2+1)(y2y+1)
Hence, factorization of y7+y is y(y2+1)(y2y+1) and their factors are the following:
y
y2+1
y2y+1

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