Identify zeros from factorizations and use them to sketch polynomial graphs.
Find zeros from a factored polynomial by setting each factor equal to zero
Problem
Find the zeros of \((x~-~3)(x~+~2)(2x~-~1)\).
Big Picture
What this problem is really about
Factored form turns zero-finding into three small linear equations. Since a product equals zero when any factor is zero, we’ll set each factor separately equal to zero and solve, including division for the factor with a coefficient on x. The resulting solutions are zeros because each makes the entire product vanish.
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