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

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

Medicim6 · Accepted Answer

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)(a2−ab+b2)  Hence p=(x+1)[x2−(x)(1)+12](x+1)  p=(x+1)(x2−x+1)(x+1)  p=(x+1)(x+1)(x2−x+1)  Hence x4+x3+x+1=(x+1)(x+1)(x2−x+1)

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

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