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I'm having trouble factorising questions like these.

Sketch the graph of P(x) = x4 - 4x2 + 4

The y intercept is obviously (0,4) but I cant find the x intercepts without factorising it first. I try subbing in values for x (e.g.: P(1), P(2), P(-1), etc.) but nothing turns up equalling zero.

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1 Answer

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A hint when dealing with these special types of quartics:

Let x2 = a, to simplify it into a quadratic in a: a2 - 4a + 4

Now that you can factorise that: (a-2)2) = (x2 - 2)2

Using difference of perfect squares (DOPS): [(x - sqrt(2))(x + sqrt(2))]2 - there are your factors!

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