document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #352237 by KMST(5328) $\"\"$ $\"About$

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Your cubic, P(x) must be divisible by (x-5) because x=5 is a root.
\n" ); document.write( "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.
\n" ); document.write( "The same reasoning (or theorem) applies to show that (x+2) and (x-3) are factors.
\n" ); document.write( "P(x)=a(x+2)(x-3)(x-5) where a is a number that is not zero. \n" ); document.write( "

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