Factor each polynomial completely. If the polynomial cannot be factored,

Inyalan0

Inyalan0

Answered question

2021-12-10

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
x4+x3+x+1

Answer & Explanation

Medicim6

Medicim6

Beginner2021-12-11Added 33 answers

Step 1
Given:
Let p=x4+x3+x+1
To Find: To factorise the given polynomial
Step 2
Solution:
p=x4+x3+x+1
p=x3(x+1)+1(x+1)
p=(x3+1)(x+1)
p=(x3+13)(x+1)
We know that a3+b3=(a+b)(a2ab+b2)
Hence p=(x+1)[x2(x)(1)+12](x+1)
p=(x+1)(x2x+1)(x+1)
p=(x+1)(x+1)(x2x+1)
Hence x4+x3+x+1=(x+1)(x+1)(x2x+1)

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