3.54: Cubic factors: sketch, inequality, modulus graph

0606/22/M/J/24 — Question 1 · 6 marks

(a)
On the axes, sketch the graph of y=(x−2)(x+5)(3x−1)y = (x - 2)(x + 5)(3x - 1), stating the intercepts with the coordinate axes.
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(b)(i)
Solve the inequality (x−2)(x+5)(3x−1)⩽0(x - 2)(x + 5)(3x - 1) \leqslant 0.
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(b)(ii)
On the axes below, sketch the graph of y=∣(x−2)(x+5)(3x−1)∣y = \bigl|(x - 2)(x + 5)(3x - 1)\bigr|.
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