Math  /  Algebra

QuestionWatch the video and then solve the problem given below. Click here to watch the video. Find the zeros of the function, and their multiplicities. f(x)=x35x2x+5f(x)=x^{3}-5 x^{2}-x+5
The zeros of the function are x=1,5,1x=1,5,-1. (Use a comma to separate answers as needed.) Each zero has multiplicity \square

Studdy Solution
To determine the multiplicities, factor the polynomial.
Given that the zeros are x=1,5,1 x = 1, 5, -1 , the polynomial can be expressed as:
f(x)=(x1)(x5)(x+1) f(x) = (x - 1)(x - 5)(x + 1)
Each factor is distinct, indicating that each zero has a multiplicity of 1.
The zeros of the function are x=1,5,1 x = 1, 5, -1 , each with multiplicity 1 1 .

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