Question

divide
p4+p3-p2+1 by p-1

Answer 1

Answer:

$\red {( p^{4}+p^{3}-p^{2}+1 ) \div (p-1)}$

$= \green {(p-1)(p^{3}+2p^{2}+p+1)+2}$

Step-by-step explanation:

$\red {( p^{4}+p^{3}-p^{2}+1 ) \div (p-1)}$

p-1 )p⁴+p³-p²+0+1(p³+2p²+p+1

*****p⁴-p³

_______________

********2p³ - p²

******** 2p³ - 2p²

_______________

************** p² + 0+ 1

************** p²- p

_________________

****************** p + 1

****************** p - 1

__________________

Remainder ( 2 )

Dividend = p⁴ + p³ - p² + 1 ,

Divisor = p - 1,

Quotient = p³ + 2p² +p + 1,

Remainder = 2

Therefore.,

$\red {( p^{4}+p^{3}-p^{2}+1 ) \div (p-1)}$

$= \green {(p-1)(p^{3}+2p^{2}+p+1)+2}$

•••

Answer 2

QUOTIENT: p³ + 2p² + p - 1

REMINDER: 0