Question

find the sum of the remainders when the polynomial p(x) =x3 - 3x2 + 4x-9 is divided by (x-1) and (x+2).

Answer 1

Hii friend,

G(X) = X-1

X = 1.

P(X) = X³-3X²+4X-9

P(1) = (1)³ - 3 × (1)² + 4 × 1 -9

= 1 - 3 + 4 - 9 = 5 - 12 = -7

Again,

G(X) = (X+2)

X = -2

P(X) = X³-3X²+4X -9

P(-2) = (-2)³ -3 × (-2)² + 4 × -2 -9

= -8 -3 × 4 -8 -9

= -8-12-17 = -37

Therefore,

Sum of the remainders = (-7) + (-37) = -7 -37 = -44

HOPE IT WILL HELP YOU..... :-)

Answer 2

using reminder thereom
x-1 = 0. x+2 = 0
x = 1 x= -2

fill the value of x in p(x)

x³-3x²+4x-9

= (1)³-3(1)²+4(1)-9

= 1-3+4-9

= 5 -12

= -7

R1 = -7

x³-3x²+4x-9

= (-2)³-3(-2)²+4(-2)-9

= -8-3(4)-8-9

= -8-12-17

= -37

R2 = -37

R1+R2
= -7+(-37)
= -7-37
= -44