Factor the polynomial P(x)=x3+2x2−8x and use the factored form to find the zeros. Then sketch the graph.
P(x)=x3+2x2−8x=x(x2+2x−8)Factor out x=x(x+4)(x−2)Simplify
Since the function has an odd degree of 3 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=x(x+4)(x−2)
By zero product property, we have
x=0,x+4=0 and x−2=0
Thus, the x-intercept are x=0,−4 and 2
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