Question

Perform the indicated operation: (a4-3a²-a?-1)-(-2a4+2a +a?+2)​

Answer 1

Let a4+2a3+3a2+2a+1=(ba2+ca+d)2a4+2a3+3a2+2a+1=(ba2+ca+d)2 where b,c,d∈Rb,c,d∈R

Observe that

(ba2+ca+d)2=b2a4+2bca3+(2bd+c2)a2+2cda+d2(ba2+ca+d)2=b2a4+2bca3+(2bd+c2)a2+2cda+d2

Comparing coefficient of like terms, we get

b2=1⇒b=±1b2=1⇒b=±1

bc=1⇒c=±1bc=1⇒c=±1

±2d+1=3⇒d=±1±2d+1=3⇒d=±1

Thus,

a4+2a3

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