Question

What is the remainder when (x^3 – 58) ÷ (x – 4) ?

Answer 1

Remainder Theorem: when \(p(x)\) is divided by \(x - k\), then the remainder is \(p(k)\).

Answer 2

There are two methods for this

1) Long-division method
2) remainder theorem

Answer 3

i dont recall the remainder theorem, care to explain?

Answer 4

let x - 4 = 0

x = 4

p(x) = x^3-58

put x = 4

p(4) = 0 = 4^3 - 58

Answer 5

Thus, you have to calculate \(f(4)\) where \(f(x) = x^3 - 58\)

Answer 6

\[x=\sqrt[3]{58}\]

Answer 7

\[\large{p(4) = 4^3-58=Remainder*}\]
\[\large{64-58=Remainder}\]

Answer 8

sorry I meant in my earlier post p(4) = remainder \(\ne 0\) ...

@kakrazz
hence we will get remainder = ?

Answer 9

OH, okay thank you! I have never learned the remainder theorem. Thank you guys

Answer 10

remainder is 6

Answer 11

so 6

Answer 12

very good @kakrazz good work

Answer 13

yes

Answer 14

thank you! i have like.. 8 more questions to ask on openstudy hahaha

Answer 15

No problem kakrazz you can also use "Long-division" method ...

BUT remainder theorem is best and easiest

Answer 16

it seemed really easy too

Answer 17

correct... it's easy but it's use is very wide