ACT Preparation / Unit 11 ACT 1020 short lesson, about 20 seconds
Zeros and Multiplicity
Captions available
The idea
A factor (x − c)ⁿ gives the zero c with multiplicity n. At a zero of odd multiplicity the graph crosses the x-axis; at even multiplicity it touches and turns.
In practice
f(x) = (x − 1)²(x + 3) touches at 1 and crosses at −3.
Where people slip
A zero at −3 means a factor of x + 3.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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