monic polynomial EX2. please help! (1 Viewer)

[carol chow]

prove the theorem:
if x=r is an integral zeor of the monic polynomial
P(x)=xⁿ+a_n-1x^n-1+...+a_o, then r must be a factor of a₀


please help me with the question. I was overseas in the first 2 school weeks. I can't figure out how to sort the question. I know I am not smart, but.... please help

 

[zeebobDD]

P(r) =0 therefore rn+rn-1rn-1+...+ ao =0
therefore ao= -( rn+rn-1rn-1 +..)
= ao=-r(1n +1n-11n +…)
Therefore r is a factor of ao

im nt sure if proving it is a factor is the same as r dividing ao correct me if im wrong:/

 

[Carrotsticks]

im nt sure if proving it is a factor is the same as r dividing ao correct me if im wrong:/

That's right.

ie: 12 = 4 x 3

Thus, 3 is a factor of 12.

 

[Nooblet94]

P(r) =0 therefore rn+rn-1rn-1+...+ ao =0
therefore ao= -( rn+rn-1rn-1 +..)
= ao=-r(1n +1n-11n +…)
Therefore r is a factor of ao

im nt sure if proving it is a factor is the same as r dividing ao correct me if im wrong:/

Yep, that's right.

 

[math man]

P(r) =0 therefore rn+rn-1rn-1+...+ ao =0
therefore ao= -( rn+rn-1rn-1 +..)
= ao=-r(1n +1n-11n +…)
Therefore r is a factor of ao

im nt sure if proving it is a factor is the same as r dividing ao correct me if im wrong:/

To make proof more concrete you shouldn't just conclude r is a factor , you should add:

Since we have found that is the product of r and another number, say B, where
r must be a factor of then
add QED or little square or just even move on to another question

 

[zeebobDD]

To make proof more concrete you shouldn't just conclude r is a factor , you should add:

Since we have found that is the product of r and another number, say B, where
r must be a factor of then
add QED or little square or just even move on to another question

thanks maaath maan!