Polynomials Question (1 Viewer)

[bujolover]

P(x) is a polynomial of degree 3.
Find P(x), given that :
- y = P(x) is an odd function.
- (x - 2) is a factor of P(x).
- when P(x) is divided by (x + 4), the remainder is 96.

I don't get how to do it, and the given solution doesn't make sense to me because the first line says to let P(x) = ax³ + bx. Shouldn't it be let P(x) = ax³ + bx² + cx + d? How do they know that b and c are 0?

 

[jazz519]

P(x) is a polynomial of degree 3.
Find P(x), given that :
- y = P(x) is an odd function.
- (x - 2) is a factor of P(x).
- when P(x) is divided by (x + 4), the remainder is 96.

I don't get how to do it, and the given solution doesn't make sense to me because the first line says to let P(x) = ax³ + bx. Shouldn't it be let P(x) = ax³ + bx² + cx + d? How do they know that b and c are 0?

Straight off the b and c are zero because its a odd function (these can only have the odd x to the power so i.e. means like three and one and not the two and zero). This can also be proven algebraically