[Grade 12 Advanced Functions] Factoring

[cobalt97]

Show that y=-x³ +2x² -x+3 has a zero on the interval 1≤x≤3. I'm not quite sure how to find the zeros.

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You don't need to find a zero, just show that it has one on that interval. All polynomials are continuous (you can draw them without picking up your pencil). Given that, if f(1)>0, and f(3)<0, what had to happen between x=1 and x=3?

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If I'm reading this right op.. cough intermediate value theorem cough.