Question

x⁵+x⁴+x³+x²+x+1 by x³+1 divide​

Answer 1

Step-by-step explanation:

If f(x)=x4+x3+x2+x+1 , what will be the remainder when f(x5) is divided by f(x) ?

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Shambhu Bhat

Answered 1 year ago

If f(x) = x⁴ + x³ + x² + x + 1, what will be the remainder when f(x⁵) is divided by f(x)?

,……………………………………………………………………………………………….

Let

f(x5)=x20+x15+x10+x5+1

=(A(x−1)+B)g(x)(x4+x3+x2+x+1)+R(x)

=Ag(x)(x5–1)+Bg(x)(x4+x3+x2+x+1)+R(x)

where R(x) is the remainder.

Setting x5=1

1+1+1+1+1=Bg(x)(x4+x3+x2+x+1)+R(x)⟹B=0&R(x)=5