Question

x-1)3x^ 4 -4x^ 3 -3x-1
by long division method​

Answer 1

Step-by-step explanation:

Given:-

3x^ 4 -4x^ 3 -3x-1

To find :-

Divide 3x^ 4 -4x^ 3 -3x-1 by x-1?

Solution:-

Given Polynomial = 3x^ 4 -4x^ 3 -3x-1

It can be written as 3x^ 4 -4x^ 3+0x^2 -3x-1

Given divisor = x-1

Long Division:-

x-1) 3x^ 4 -4x^ 3 + 0x^2 -3x-1(3x^3 - x^2 -x-4

3x^ 4 -3x^ 3

(-) (+)

____________________

0 - x^ 3 + 0x^ 2

- x^ 3 + x^ 2

(+) (-)

_____________________

0 - x^ 2 - 3x

- x^ 2 + x

(+) (-)

______________________

0 -4x -1

-4x +4

(+) (-)

_______________________

0 -5

________________________

Quotient = 3x^3 - x^2 -x-4

Remainder = -5

Answer:-

Quotient = 3x^3 - x^2 -x-4

Remainder = -5

Check:-

Dividend = Divisor× Quotient+Remainder

=> (x-1)×(3x^3 - x^2 -x-4)+(-5)

=>x(3x^3 - x^2 -x-4)-1(3x^3 - x^2 -x-4)-5

=> 3x^4 -x^3 -x^2 -4x -3x^3+x^2+x+4-5

=> 3x^4-4x^3+0x^2-3x-1

=> 3x^4-4x^3-3x-1

=> Given Polynomial

Verified the given relation.

Used Method:-

Long Division Method

Used formula:-

Dividend = Divisor× Quotient+Remainder