Answer:
the degree of the polynomial
Step-by-step explanation:
Given
Polynomial equation
Required
What does the sum of the multiplicities add up to
To answer this question, I'll make use of the following polynomial.
[tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex]
When factorized, the polynomial is:
[tex]p(x) = (x - 1)(x - 3)(x-3)[/tex]
[tex]p(x) = (x - 1)(x - 3)^2[/tex]
x-1 can be expressed as [tex](x - 1)^1[/tex]
So, we have:
[tex]p(x) = (x - 1)^1(x - 3)^2[/tex]
The sum of multiplicity (M) of the equation is 3.
This is so because
[tex]x - 1[/tex] occurred one time in [tex]p(x) = (x - 1)(x - 3)^2[/tex]
[tex]x - 3[/tex] occurred two times in [tex]p(x) = (x - 1)(x - 3)^2[/tex]
[tex]Sum= 1 + 2[/tex]
[tex]Sum= 3[/tex]
The degree of [tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex] or [tex]p(x) = (x - 1)^1(x - 3)^2[/tex] is 3.
This implies that:
[tex]Sum = Degree = 3[/tex]
Hence: Option (a) answers the question
