Consider the graph of m(x). Given that (x+1)
is a factor of m(x), which of the following could be the multiplicity of (x+1)
?
Option #1: −1
Option #2: 0
Option #3: 1
Option #4: 2
(1 point)
Option #
gives a possible multiplicity of (x+1)
.
The correct option that gives a possible multiplicity of (x+1) is:
Option #3: 1
To determine the possible multiplicity of (x+1), we need to analyze the given information.
If (x+1) is a factor of m(x), then when we divide m(x) by (x+1), the remainder should be zero. This implies that (x+1) is a root of m(x) and has a multiplicity at least 1.
Now, let's consider the options:
Option #1: -1
A negative multiplicity does not make sense as multiplicities are non-negative integers.
Option #2: 0
A multiplicity of 0 means that (x+1) is not a root of m(x), which contradicts the given information that (x+1) is a factor of m(x).
Option #3: 1
A multiplicity of 1 is possible since (x+1) being a factor implies it is also a root of m(x).
Option #4: 2
A multiplicity of 2 is also possible. This means that (x+1) is a repeated root of m(x) and appears twice in the factorization.
Based on the analysis, both option #3 and option #4 could be the multiplicity of (x+1).
To determine the multiplicity of the factor (x+1) in the graph of m(x), we need to understand what multiplicity represents for a factor.
In a polynomial, the multiplicity of a factor represents the number of times that factor occurs in the polynomial. It tells us how many times the factor is repeated or how many times it is a root.
To find the possible multiplicity of (x+1), we need to analyze the graph of m(x) given that (x+1) is a factor.
Let's consider the options:
Option #1: -1 as the multiplicity of (x+1)
A multiplicity of -1 is not possible because multiplicity must be a positive integer or zero.
Option #2: 0 as the multiplicity of (x+1)
A multiplicity of 0 means that (x+1) is not a factor of m(x). Since the question states that (x+1) is a factor, this option is not valid.
Option #3: 1 as the multiplicity of (x+1)
A multiplicity of 1 means that (x+1) appears once as a factor. This is a possible option, as it aligns with the given information.
Option #4: 2 as the multiplicity of (x+1)
A multiplicity of 2 means that (x+1) appears twice as a factor. This is also a possible option.
Therefore, both options #3 and #4 could be the multiplicity of (x+1) in the graph of m(x).