Factor the polynomial P(x)=x6−2x3+1 and use the factored form to find the zeros. Then sketch the graph.
Since the function has an even degree of 4 and a positive leading coefficient, its end behaviour is y→∞ as x→−∞ and y→∞ as x→∞. To find the x intercepts (or zeros), we set y=0.
0=x6−2x3+10=w2−2w+1Let w=x30=(w−1)2Perfect Squarew=1Substitutew=x3x3=1
Thus, the x-intercept are x=1
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