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How do you factor completely x31?

Answer
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Hint:
To find out factors of the above question, we will solve the cubes of the given terms with the help of identities and then put the given values into the identities. In the first method, we will use the identity in which cubes of two numbers are subtracted and in the second method, we use the identity in which cubes of two numbers are added.

Formula used:
a3b3=(ab)(a2+ab+b2)

Complete step by step solution:
We can factor x31 by using formula a3b3=(ab)(a2+ab+b2) .
Here we will consider a=x
And b=1 as we know that 13=1
Put these values into the formula.
x3(1)3=(x+(1)3)(x2+x(1)+(1)2)
Simplify above equation
(x1)(x2+x+1)

Hence, (x1) and (x2+x+1) are two factors of x31.

Note:
Second method to solve above question:
Formula used:
a3+b3=(a+b)(a2ab+b2)
Complete step by step solution:
We can factor x31 by using formula a3+b3=(a+b)(a2ab+b2) .
Here we will consider a=x
And b=1 as we know that (1)3=1
Put these values into a formula.
x3+(1)3=(x+(1))(x2x(1)+(1)2)
Simplify above equation
(x1)(x2+x+1)
Hence (x1) and (x2+x+1) are two factors of x31 .
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