Question

when p(x)=ax^3+bx+c is divided by (x-1) the remainder is -4. when p(x) is divided by (x^2-4) the remainder is -4x+3.find a b and c

Answer 1

did you attempt to do the long division?

Answer 2

you there?

Answer 3

use remainder theorema, :
p(x) = ax^3+bx+c
if p(x) divided (x-1), the remainder is -4. it means
p(1) = -4
a(1)^3 + b(1) + c = -4
a + b + c = -4 ... (1)

next, x^2-4 = (x+2)(x-2)
if p(x) divided (x+2), the remainder is -4x+3. it means
p(-2) = -4(-2) + 3
p(-2) = 11
a(-2)^3 + b(-2) + c = 11
-8a - 2b + c = 11 ... (2)

if p(x) divided (x-2), the remainder is -4x+3. it means
p(2) = -4(2) + 3
p(2) = -5
a(2)^3 + b(2) + c = 11
8a + 2b + c = -5 ... (3)

now, there are three equation with 3 variables... just find solution of them... maybe u can use subtitution and elimination method

Answer 4

yeah i am here

Answer 5

that's actually the long way in this case... but whatever.

Answer 6

sorry, there is a typo error before get 3th equation :)
it should be :
a(2)^3 + b(2) + c = -5 (not 11)
8a + 2b + c = -5 ... (3)

Answer 7

thanks so much

Answer 8

welcome...