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Question

Find all zeros of the polynomial P(x)=x33x26x+8 knowing that x = 1 is a zero of the polynomial.

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Solution

We can see at x=1,f(1)=0
(x1))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x33x26x+8(x22x8x3x2________________2x26x2x3+2x________________8x+88x+8________________

f(x)=(x1)(x22x8)

=(x1)(x+2)(x4)

So all zeros of f(n) are 1,2,4

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