Identify the multiplicities of the linear factors of h(x)=(x+4)(x−1)^2(x+3)^5 .(1 point)
1. The multiplicity of (x+4) is 0, the multiplicity of (x-1) is 2, the multiplicity of (x+3) is 5.
2. The multiplicity of (x+4) is -4, the multiplicity of (x-1) is 1, the multiplicity of (x+3) is -3.
3. The multiplicity of (x+4) is 4, the multiplicity of (x-1) is -1, the multiplicity of (x+3) is 3.
4. The multiplicity of (x+4) is 1, the multiplicity of (x-1) is 2, the multiplicity of (x+3) is 5.
The correct answer is:
4. The multiplicity of (x+4) is 1, the multiplicity of (x-1) is 2, the multiplicity of (x+3) is 5.
The correct answer is 4. The multiplicity of (x+4) is 1, the multiplicity of (x-1) is 2, and the multiplicity of (x+3) is 5.
To identify the multiplicities of the linear factors of the given polynomial h(x), we can look at the exponents of each linear factor.
In the given polynomial h(x) = (x+4)(x-1)^2(x+3)^5, the linear factors are (x+4), (x-1), and (x+3).
The multiplicity of a linear factor is determined by the exponent of that factor.
So, the multiplicity of (x+4) is 1.
The multiplicity of (x-1) is 2.
The multiplicity of (x+3) is 5.
Therefore, the correct answer is: 4. The multiplicity of (x+4) is 1, the multiplicity of (x-1) is 2, the multiplicity of (x+3) is 5.