polynomials (1 Viewer)

[maths lover]

sorry guys but i need help with another question.
p(x) is a odd polynomial of degree 3. it has (x+4) as a factor and when divided by (x-3) the remainder is 21. find p(x).
i don't even know where to start for this question.

 

[funnytomato]

sorry guys but i need help with another question.
p(x) is a odd polynomial of degree 3. it has (x+4) as a factor and when divided by (x-3) the remainder is 21. find p(x).
i don't even know where to start for this question.

P(x) is odd , so there wouldn't be any constant or x^(even number) terms
then set the coefficients of the odd powers (only x and x^3)to be some pronumerals (say a and b)

then use factor and remainder theorems to find out these values

 

[maths lover]

P(x) is odd , so there wouldn't be any constant or x^(even number) terms
then set the coefficients of the odd powers (only x and x^3)to be some pronumerals (say a and b)

then use factor and remainder theorems to find out these values

ok i get it but why wouldn't there be a constant.

 

[funnytomato]

ok i get it but why wouldn't there be a constant.

if there is some non-zero constant , say c
let P(x)= ax^3 + bx + c
then P(-x)= a(-x)^3 +b(-x) + c = -ax^3 - bx + c =/= -P(x)

 

[funnytomato]

P(-x) = -P(x) only when c=0 , which means it cannot have a constant term to be an odd function

 

[maths lover]

i really appreciate it thanks heaps.