Which of the graphs below is the graph of \(y = 3 - 2{\left( {x + 1} \right)^3}\) ?

Which of the graphs below is the graph of \(y = {\left( {x + 1} \right)^2}{\left( {2 - x} \right)^2}\) ?

Which of the graphs below is the graph of \(y = \left( {x + 1} \right){\left( {2 - x} \right)^3}\) ?

Which of the graphs below is the graph of \(y = {\left( {x + 1} \right)^3}{\left( {2 - x} \right)^2}\) ?

Sketch the graph of \(y = (x + 1)(x - 2)(x - 1)\) showing all \(x\) and \(y\) intercepts.

Factories \(P(x) = {x^2} - {x^4}\), find the zeros of \(P(x)\) and sketch the polynomial.

Given that \(x = 2\) is the zero of the polynomial \(P(x) = {x^3} - 3x - 2\), find the other zeros, sketch the polynomial and hence solve the inequality \({x^3} - 3x - 2 > 0\).

Find the roots of the polynomial \(P(x) = {x^4} + 3{x^3} - 3{x^2} - 7x + 6\) given that \(x = 1\) is a double root. Hence sketch \(y = P(x)\).

Sketch the graph of \(y=(x+1)^3(2-x)\) showing all \(x\) and \(y\) intercepts and point(s) of inflexion.

Sketch the graph of \(y=(x+1)(x-2)(x-1)\) showing all \(x\) and \(y\) intercepts.

Sketch the graph of \(y=x(x+2)(x-1)^2\) showing all \(x\) and \(y\) intercepts and point(s) of contact.

Find the zeros of the polynomial \(P(x)=5 x(x-1)^3\) and sketch the polynomial.

Factorise \(P(x)=x^3-x^2-x+1\), find the zeros of \(P(x)\) and sketch the polynomial.

Find the zeros of the polynomial \(P(x)=\dfrac{1}{3} x^3(x-2)^2(x+2)\) and sketch the polynomial.

Find the zeros of the polynomial \(P(x)=-x^4+8 x^2-16\) and sketch the polynomial.

The polynomial \(P(x)=x^3+p x^2+q x+r\) has roots \(0,2,-2\).

(i) Find \(p, q\) and \(r\).
(ii) Without calculus sketch the graph of \(y=P(x)\).
(iii) Hence, solve the inequality \(x^3-4 x \geq 0\).

Find the zeros of the polynomial \(P(x)=x(x+2)(x-1)^3\) and sketch \(y=P(x)\)