Question

Divide (-1+x^4) by (-1+x) and verify your answer.

Answer 1

Hello..
Answer..

$write \: the \: divisor( - 1 + x) \: and \: e \: dividend \: ( - 1 + {x}^{2} ) \: in \: the \: standard \: form.$
$dividendo \: = {x}^{2} - 1 \: and \: divisor \: = x - 1 \\ \\ in \: the \: dividendo \: the \: terms \: involving \: {x}^{3} and \: {x}^{2} \: are \: missing \: so \: we \: use \: 0 \: as \: the \: coefficient \: of \: each \: missing \: term.$
Verification :
Remainder=0
Dividendo =Divisor multiplied by Quotient,
ie,.
${x}^{2} - 1 = (x - 1)( {x}^{3} + x + 1)$
RHS:
$(x - 1)( {x}^{3} + {x}^{2} + x + 1) = {x}^{4} + {x}^{3} + {x}^{2} + x - {x}^{3} - {x}^{2} - x - 1 \\ = {x}^{4} - 1$
= LHS
verified...

Hope it helped ☺ ☺ ☺

Answer 2

Hii
Here is your answer in the pic..

Sorry I don't know to verify.. ☺ ☺ ☺