Identify the multiplicities of the linear factors of h(x)=(x+4)(x−1)2(x+3)5 .(1 point)
Responses
The multiplicity of (x+4) is 0, the multiplicity of (x−1) is 2, and the multiplicity of (x+3) is 5.
The multiplicity of left parenthesis x plus 4 right parenthesis is 0, the multiplicity of left parenthesis x minus 1 right parenthesis is 2, and the multiplicity of left parenthesis x plus 3 right parenthesis is 5.
The multiplicity of (x+4) is 4, the multiplicity of (x−1) is −1, and the multiplicity of (x+3) is 3.
The multiplicity of left parenthesis x plus 4 right parenthesis is 4, the multiplicity of left parenthesis x minus 1 right parenthesis is negative 1 , and the multiplicity of left parenthesis x plus 3 right parenthesis is 3.
The multiplicity of (x+4) is 1, the multiplicity of (x−1) is 2, and the multiplicity of (x+3) is 5.
The multiplicity of left parenthesis x plus 4 right parenthesis is 1, the multiplicity of left parenthesis x minus 1 right parenthesis is 2, and the multiplicity of left parenthesis x plus 3 right parenthesis is 5.
The multiplicity of (x+4) is −4, the multiplicity of (x−1) is 1, and the multiplicity of (x+3) is −3.
The multiplicity of (x+4) is 1, the multiplicity of (x−1) is 2, and the multiplicity of (x+3) is 5.
The multiplicity of (x+4) is 1, the multiplicity of (x−1) is 2, and the multiplicity of (x+3) is 5.
The correct answer is:
The multiplicity of (x+4) is 1, the multiplicity of (x−1) is 2, and the multiplicity of (x+3) is 5.
To determine the multiplicities of the linear factors in the given polynomial, h(x)=(x+4)(x−1)2(x+3)5, we need to look at the exponents of each linear factor.
In the expression (x+4), the exponent is 1. This means that the factor (x+4) appears once, so the multiplicity is 1.
In the expression (x−1)2, the exponent is 2. This means that the factor (x−1) appears twice, so the multiplicity is 2.
In the expression (x+3)5, the exponent is 5. This means that the factor (x+3) appears five times, so the multiplicity is 5.
Therefore, the multiplicity of (x+4) is 1, the multiplicity of (x−1) is 2, and the multiplicity of (x+3) is 5.