Question 1172364: Sam is working on some polynomial factorizations in the form of x^2 + px + q , where p and q are nonzero integers. His work is as follows:
x^2 −2x−3=(x−3)(x+1)
x^2 +5x+6=(x+2)(x+3)
x^2 −7x+10=(x−2)(x−5)
x^2 +6x+8=(x+2)(x+4)
x^2 −8x+12=(x−2)(x−6)
x^2 +9x+18=(x+3)(x+6)
He concludes that if p and q are coprime, then the factors a and b are also coprime. If p and q are not coprime, then the factors a and b are not coprime, either.
Is his conclusion correct? Explain please.
Answer by ikleyn(52810)   (Show Source):
You can put this solution on YOUR website! .
Hello, from your post, it is UNCLEAR to me what you call as "the factors a and b" ?
They are not defined anywhere in your post, making it non-sensical.
If you mean "a" and "b" as linear binomials, then they ALWAYS are coprime as polynomials, until they coincide.
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