Rational root theorem examples. Applications to solving polynomial equations. Factorisation with long division or equating coefficients. Effect of transformations on the position of roots. Power point presentation.

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The Rational Root Theorem is a useful tool in algebra for finding potential rational roots (or solutions) of a polynomial equation with integer coefficients. It helps narrow down the search for roots, making the process more efficient. Suppose that a polynomial equation with integer coefficients has the root **p/q** , where **p** and **q **are integers. Then **p** must be a factor of the **constant term **of the polynomial and **q** must be a factor of the **leading ****coefficient. **Once you have identified the possible rational roots, you can test them using methods like synthetic division or polynomial long division to see if they are actual roots of the polynomial equation.