Question

Guys.. please prove these... using Remainder theoram.. fake ans will be reported​

Answer 1

Answer:

According to factor theorem, the dividend is equal to the sun of the product of the quotient and the divisor and the remainder.

$p(x) = q(x).d(x) + r(x)$

p(x) is the dividend, q(x) is the quotient, d(x) is the divisor and r(x) is the remainder.

Here,

$p(x) = {3x}^{4} - {4x}^{3} - 3x - 1$

$q(x) = {3x}^{3} - {7x}^{2} + 7x - 10$

$d(x) = x + 1$

$r(x) = 9$

On substituting,

${3x}^{4} - {4x}^{3} - 3x - 1 = ({3x}^{3} - {7x}^{2} + 7x - 10)(x + 1) + 9$

Solve RHS:

$( {3x}^{3} - {7x}^{2} + 7x - 10)(x + 1) + 9$

$= {3x}^{4} - {7x}^{3} + {7x}^{2} - 10x + {3x}^{3} - {7x}^{2} + 7x - 10 + 9$

$= {3x}^{4} - {4x}^{3} - 3x - 1 = p(x)$

Hence, proved.