(a) On the axes, sketch the graph of \(y=(1-x)(x-5)(2x-5)\), stating the intercepts with the axes.

(b) Hence solve the inequality \((1-x)(x-5)(2x-5)\leqslant0\).

The diagram shows the graph of \(y=(x+1)(x-1)(x-2)\). Use the graph to solve the inequality \((x+1)(x-1)(x-2)\lt 1\).

(a) On the axes, sketch the graph of \(y=-\frac{1}{5}(x+2)(2 x-1)(x+5)\), stating the intercepts with the axes.

(b) Hence solve the inequality \(-\frac{1}{5}(x+2)(2 x-1)(x+5) \geqslant 0\).

The diagram shows the graph of the cubic polynomial \(y=f(x)\).

(a) Find an expression for \(f(x)\) in factorised form. Write each linear factor with its coefficients as integers.

(b) Write down the values of \(x\) such that \(f(x)\lt 0\).

The diagram shows the graph of \(y=f(x)\), where \(f(x)=a(x+b)^2(x+c)\) and \(a\), \(b\) and \(c\) are integers.

(a) Find the value of each of \(a\), \(b\) and \(c\).

(b) Hence solve the inequality \(f(x)\leqslant -1\).

(a) On the axes, sketch the graph of

\(y=5(x+1)(3x-2)(x-2),\)

stating the intercepts with the coordinate axes.

(b) Hence find the values of \(x\) for which

\(5(x+1)(3x-2)(x-2)\gt0.\)

(a) Sketch the graph of

\(y=-3(x-2)(x-4)(x+1),\)

showing the coordinates of the points where the curve intersects the coordinate axes.

(b) Hence find the values of \(x\) for which

\(-3(x-2)(x-4)(x+1)\gt 0.\)

The diagram shows the graph of a cubic curve \(y=f(x)\).

(a) Find an expression for \(f(x)\).

(b) Solve \(f(x)\leq0\).

(a) On the axes below, sketch the graph of

\(y=(x-2)(x+1)(3-x),\)

stating the intercepts on the coordinate axes.

(b) Hence write down the values of \(x\) such that

\((x-2)(x+1)(3-x)\gt 0.\)