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NSW · Maths Extension 1
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§-Quick questions
NSWMaths Extension 1Functions (ME-F1, ME-F2)

Quick questions on Polynomial and rational inequalities: sign analysis, critical points and excluded values

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is build the sign diagram, stage by stage?
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A sign diagram is the cleanest way to show your working, and markers can follow it at a glance. Below, the inequality x3−4x≥0x^3 - 4x \ge 0 is solved by building the sign diagram one stage at a time. Factor first: x3−4x=x(x−2)(x+2)x^3 - 4x = x(x - 2)(x + 2), so the critical values are x=−2,0,2x = -2, 0, 2.
What is sign sloppiness in factored form?
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If the leading coefficient is negative, every interval sign flips. Factor out the negative explicitly: −x2+3x−2=−(x−1)(x−2)-x^2 + 3 x - 2 = -(x - 1)(x - 2).

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