The function \( h(x) = (x+4)(x-1)^2(x+3)^5 \) is expressed in terms of its linear factors. The multiplicities of the linear factors can be identified from the exponents of each factor in the expression.
- The factor \( (x+4) \) has a multiplicity of \( 1 \) because it is raised to the power of \( 1 \).
- The factor \( (x-1)^2 \) has a multiplicity of \( 2 \) because it is raised to the power of \( 2 \).
- The factor \( (x+3)^5 \) has a multiplicity of \( 5 \) because it is raised to the power of \( 5 \).
Therefore, the multiplicities of the linear factors are:
- For \( (x+4) \): 1
- For \( (x-1) \): 2
- For \( (x+3) \): 5
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