Question

if the polynomials px³+4x²+3x-4 and x³-4x+p are divide by x-3 , then the remainder in each case is the same . Find the value of P​

Answer 1

${\huge{\boxed{\mathcal\star{\red{Answer}}}}}$

Given Polynomials

$=> f (x) = Px³ + 4x² + 3x - 4$

$\:=> g (x) = x³ - 4x + P \\ and \: the \: zero \: of \: x - 3\: is '3'.$

$=> f (x) = g (x)$

$=> f (3) = g (3)$

$f (3) =$

$= > P \: (3)³ + 4 \: (3)² \\ + \: 3 \: (3) - 4$

$=> P (27) + 4 (9) + 9 - 4$

$=> 27 P + 36 + 9 - 4$

$f(3) = 27 P + 41$

$g \: (3) = (3)³ - 4(3) + P$

$\: \: \: \: \: \: \: \: \: \: = 27 - 12 + P$

$\: \: \: \: \: \: \: \: \: \: = 15 + P$

$\: \: \: \: \: \: \: \: \: {\large{\mathcal{\blue{=P = 45}}}}$