Question

divide 4x⁴+x³+2x²+1 by x+1

plz answer step by step
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Answer 1

Step-by-step explanation:

Given:-

4X^4+X^3+2X^2+1

To find:-

Divide 4X^4+X^3+2X^2+1 by X+1 ?

Solution:-

Given expression :4X^4+X^3+2X^2+1

Divisor = X+1

X+1) 4X^4+X^3+2X^2+1 (4X^3-3X^2+5X

4X^4+4X^3

(-) (-)

___________________

0 - 3X^3+2X^2

- 3X^3 -3X^2

(+) (+)

____________________

0 + 5X^2 +1

5X^2+5X

(-) (-)

_______________________

-5X+1 - Remainder

________________________

Answer:-

Quotient = 4X^3-3X^2+5X

Remainder = -5X+1

Check:-

Division Rule :-

Dividend = Divisor×Quotient+Remainder

=> (X+1)(4X^3-3X^2+5X) +(-5X+1)

=> X(4X^3-3X^2+5X)+1(4X^3-3X^2+5X)-5X+1

=>4X^4-3X^3+5X^2+4X^3-3X^2+5X-5X+1

=> 4X^4+X^3+2X^2+1

=> Given expression.

Verified the given relations.

Used formulae:-

Division Rule :-

Dividend = Divisor×Quotient+Remainder