#### Question

# Find the remainder of the division problem shown below.?

(x^4 - x^3 + 3x - 3) / (x-2)

#### Answer

by using the Remainder Theorem,

x-2 = 0

x = 2

substitute x=2 into x^4 - x^3 + 3x - 3,

2^4 - 2^3 + 3(2) - 3

= 11

therefore the remainder is 11...

this formula is derived from...

p(x) as initial polynomial function... (dividend)

g(x) as divisor

q(x) as quotient function

r(x) as remainder

p(x)/g(x) = q(x) + r(x)/g(x)

p(x) = q(x)g(x) + r(x)

in this case, g(x) = x-2

when x = 2, g(x) = 0

when g(x) = 0

p(x) = r(x)

therefore p(2) = r(x)

r(x) = 11

hope this helps...

Dec 6 at 0:56