Question

Divide 3x4-4x2+8x-1 by x-2 by division algorithm

Answer 1

Refer to the attacment for your desired answer :)


$\underline{\huge\text{Verification:}}$



After dividing , we've got the following results :-



$divisor = x - 2$


$dividend = 3 {x}^{4} - 4 {x}^{2} + 8x - 1$


$quotient = 3 {x}^{3} + 6 {x}^{2} + 8x + 8$


$remainder = 15$



According to Euclid's Division Lemma :-


${Dividend = Divisor\times\:Quotient + Remainder}$


Right Hand Side

$= (x - 2)(3 {x}^{3} + 6 {x}^{2} + 8x + 8) + 15$


$= 3 {x}^{4} + 6 {x}^{3} + 8 {x}^{2} + 8x - 6 {x}^{3} - 12 {x}^{2} - 16x - 16 + 15$


$= 3 {x}^{4} - 4 {x}^{2} + 8x - 1 =$Left Hand Side .

Answer 2

Answer:

divisor=x-2

Dividend = 3x4-4x2+8x-1

Ouotient=3x3+6x2+8x+8

Remainder =15

According to Euclid's Division Lemma

Dividend =Divisor×Ouotient

R.H.S=(x-2) (3x3+6x2+8x+5=15

=3x4+6x3+8x2+8c-6x3+12 x2 +7x-16+15

L.H.S =3x4-4x+8x-2-1