Question

a^4+a^2+1 by a^2+a+1

Answer 1

Step-by-step explanation:

a^4+a^2+1

-----------------------------

a^2+a+1

a^4-2+a^2-1+1

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1

a²+a+1. a²+a+1

----------- =

1

Answer 2

Answer:

a^4 - ( a² +2a +1)

= a^4 - ( a+1)²

= ( a²)² - ( a+1)²

= ( a² +a+1) ( a² -a-1) ………( polynomial factors)

So, here biquadratic expression has been factorized into 2 lower degree ie quadratic factors…

Further, since the question asked is not “factorization of a polynomial” but simply factorize the given expression ..

So, ( a² +a + 1 ) can be factorized further into lower degrees,

ie, a² +a +1

= a² +2a +1 - a

= ( a+1)² - (√a)²

= ( a +1 + √a ) ( a+ 1 -√a )

So, finally , a^4 - a² -2a -1

= ( a+1+√a) ( a+1 -√a) ( a² -a -1) ………..ANS

Step-by-step explanation:

hope it is helpful