Answer:
B
Step-by-step explanation:
If you divide x so only x and a number remains, you will get B.
[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex] has multiple zero = 4; multiplicity = 2.
" A multiple zero has the multiplicity which represents the number of times linear factor of multiple zero occur in the polynomial .Zero of the polynomial is associated with multiple zero."
According to the question,
Given,
[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex]
Simplify the given polynomial to get the multiple zero and multiplicity,
[tex]f(x) = x^{3} - 4x^{2}- 4x^{2} + 16x[/tex]
[tex]\implies x^{2} (x-4) -4x(x-4)=0\\\\\implies (x^{2} -4x)(x-4) =0\\\\\\\implies (x) (x-4)(x-4)=0\\\\\implies x(x-4)^{2} =0[/tex]
Zero is associated with x =4.
(x-4) occur twice.
Hence, multiple zero = 4 and multiplicity = 2 of the given function.
Learn more about multiple zero and multiplicity here
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