Question

Show that x-m is a factor of x^a-m^a for any positive integer a.

Answer 1

(x-m) is only a factor if m is a zero
let x=m
m^a - m^a = 0

Answer 2

thanks :)

Answer 3

that true for any value of a, not just positive integer, right ?

Answer 4

what is the answer? zero only?

Answer 5

yeah, for x-m to be the root, x^m-a^m must be = 0 for x=m

Answer 6

thanks :)

Answer 7

they want answer in form of a proof

Answer 8

uh oh what did i do :) @CarlosGP

Answer 9

carlos, please elaborate

Answer 10

Last 1 Pls help. The Polynomial 3X^2+bx-4 has x-a as a factor where a is not equal to zero. express b in terms of a. @hartnn pls help

Answer 11

since x-a is factor,
x=a will satisfy 3X^2+bx-4 =0
so, just plug in x=a in that
and solve a quadratic equation

Answer 12

3a^2+ab-4=0
can u solve this ?

Answer 13

not really.

Answer 14

you know quadratic formula ?

Answer 15

no.

Answer 16

compare the equation 3a^2+ab-4 = 0 to
Aa^2+Bb+C = 0
what are A,B, C =... ?

Answer 17

is that confusing to you ?

Answer 18

***Aa^2+Ba+C = 0

Answer 19

I'm really confused. pls show show the steps on how to answer it

Answer 20

comparing 3a^2+ab-4 = 0 with
Aa^2+Ba+C = 0
we get
A=3, B=b and C= -4

now just use the formula
\(\large a= \dfrac{-B \pm \sqrt{B^2-4AC}}{2A}\)

Answer 21

@hartnn i dont know how to use that formula \(\large a= \dfrac{-B \pm \sqrt{B^2-4AC}}{2A}\)

Answer 22

@hartnn pls help

Answer 23

just plug in A=3, B=b and C= -4
in that expression!

Answer 24

we should divide x^a-m^a by x-m

Answer 25

i think like this:
(x-m)(x^(a-1)+mx^(a-2)+m^2 x^a-3+...

Answer 26

same problem here! The Polynomial 3X^2+bx-4 has x-a as a factor where a is not equal to zero. express b in terms of a.