Question

The remainder theorem? helpp, thanks :)

Answer 1

(3x+k)^3 + (4x-7)^2 has a remainder of 33 when divided by x-3. what is k? :)

Answer 2

so substitute x = 3 into the polynomial

(3x3 +k)^3 + (4 x 3 - 7)^2 = 33

(9 + k)^3 + (5)^2 = 33

(9 +k)^3 = 8

take cube root of both sides (9 + k) = 2

I'll let you find k

Answer 3

we are given that on division we get remainder of 33 so
we have
(3x+k)^3+(4x-7)^2=(Ax^+Bx+C)(x-3)+33
A, B and C are constants
now put x=3 in the above equation
we'll get
(9+k)^3+(12-7)^2=0+33
(9+k)^3+25=33
(9+k)^3=8
8=2^3
so (9+k)^3=2^3
or 9+k=2
k=-7

Answer 4

thanks guys :) but.. why is 8=2^3?

Answer 5

(9+k)^3+(12-7)^2=0+33 (9+k)^3+25=33 (9+k)^3=8 8=2^3 so (9+k)^3=2^3 or 9+k=2 k=-

Answer 6

thanks! :)