Identify the multiplicities of the linear factors of f(x)=(x−1)2(x+4)(2x+5)
.(2 points)
The multiplicity of the factor (x−1)
is
. The multiplicity of the factor (x+4)
is
. The multiplicity of the factor (2x+5)
is
.
The multiplicity of the factor (x-1) is 2.
The multiplicity of the factor (x+4) is 1.
The multiplicity of the factor (2x+5) is 1.
The multiplicity of the factor (x−1) is 2.
The multiplicity of the factor (x+4) is 1.
The multiplicity of the factor (2x+5) is 1.
To identify the multiplicities of the linear factors of the given polynomial function f(x)=(x−1)2(x+4)(2x+5), we need to count the number of times each factor appears in the product.
1. (x−1): The factor (x−1) appears twice, so its multiplicity is 2.
2. (x+4): The factor (x+4) appears only once, so its multiplicity is 1.
3. (2x+5): The factor (2x+5) also appears only once, so its multiplicity is 1.
So, the multiplicities of the linear factors are as follows:
Multiplicity of (x−1): 2
Multiplicity of (x+4): 1
Multiplicity of (2x+5): 1