Trayvon was asked to construct a polynomial function with the following zeros and multiplicities. Which function should he write?

Question

Zero Multiplicity
x=−5
2
x=−10
5
(1 point)
Responses

f(x)=(x+5)2(x+10)5
f left parenthesis x right parenthesis equals left parenthesis x plus 5 right parenthesis squared left parenthesis x plus 10 right parenthesis superscript 5 baseline

f(x)=(x+5)5(x+10)2
f left parenthesis x right parenthesis equals left parenthesis x plus 5 right parenthesis superscript 5 baseline left parenthesis x plus 10 right parenthesis squared

f(x)=(x−5)5(x−10)2
f left parenthesis x right parenthesis equals left parenthesis x minus 5 right parenthesis superscript 5 baseline left parenthesis x minus 10 right parenthesis squared

f(x)=(x−5)2(x−10)5

Answer 1

To construct a polynomial function based on the given zeros and their multiplicities, we use the information provided:

• Zero at \( x = -5 \) with multiplicity 2 means that the factor corresponding to this zero will be \( (x + 5)^2 \).
• Zero at \( x = -10 \) with multiplicity 5 means that the factor corresponding to this zero will be \( (x + 10)^5 \).

Therefore, the polynomial function can be written as:

\[ f(x) = (x + 5)^2(x + 10)^5 \]

Thus, the correct answer is:

\[ f(x) = (x + 5)^2(x + 10)^5 \]