SOLUTION: The roots of a cubic are x=-2,x=3, and x=5. What arethe possible factors of the cubic? Explian your reasoning

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Question 536262: The roots of a cubic are x=-2,x=3, and x=5. What arethe possible factors of the cubic? Explian your reasoning
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Your cubic, P(x) must be divisible by (x-5) because x=5 is a root.
Why? When divided by (x-5) there would be a quotient Q(x) and a remainder, r (a constant), so that P(x)=(x-5)Q(x)+r, but P(5)=(0)Q(5)+r=0+r=r is zero because x=5 is a root.
The same reasoning (or theorem) applies to show that (x+2) and (x-3) are factors.
P(x)=a(x+2)(x-3)(x-5) where a is a number that is not zero.