A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division.
Part ofMathsAlgebraic and trigonometric skills
Factorise, solve or find the roots of something are all different ways of saying the same thing. You can approach all these questions in the same way. However, the answers need to be expressed in different ways.
\(f(x) = 2{x^4} + 9{x^3} - 18{x^2} - 71x - 30\)
Factorise\(f(x)\) fully.
\(\Rightarrow (x + 2)(x - 3)(x + 5)(2x + 1)\)
Solve \(f(x) = 0\)
\(\Rightarrow x = - 2,x = 3,x = - 5,x = - \frac{1}{2}\)
Find the roots of \(f(x)\)
Where does \(f(x)\) cut the \(x\)-axis?
\(\Rightarrow ( - 2,0),(3,0),( - 5,0),\left( { - \frac{1}{2},0} \right)\)
Always reread the question to ensure that you have given the answer that has been asked for.
