SETTING THE SCENE

Earlier, we used the technique of factoring to find the zeros of a quadratic expression. We can also do the reverse: knowing the zeros of a quadratic can lead to its factorisation.

PROBLEM: Consider the quadratic expression \(3x^2+x-2\). It has value zero for \(x=-1\) and for \(x=\frac{2}{3}\). Use these observations to completely factorise  \(3x^2+x-2\).

Answer: One can indeed check that \(3(-1)^2+(-1-2)\) and \((\frac{2}{3})^2+(\frac{2}{3})-2\) are each zero.

That \(x=-1\) is a zero of the expression means that \(x+1\) must be a factor of the expression. Thus …

READ MORE HERE: QUADRATICS PD Essay 4.4

(See too Edfinity.com/XXX for a robust source of curriculum practice problems for you collate, organise, and use.)

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