Find the zeros of the polynomial function and state the multiplicity of each.

f (x) = 3 (x + 7) ^2 (x - 7) ^3

a. - 7, multiplicity 2; 7, multiplicity 3

b. 4, multiplicity 1; 7, multiplicity 1; - 7, multiplicity 1

c. - 7, multiplicity 3; 7, multiplicity 2

d. 4, multiplicity 1; - 7, multiplicity 3; 7, multiplicity 3

Easy peasy

zeros are r such that (x-r)

multiplicity is how many times that factor repeats

look a it

f (x) = 3 (x+7) ^2 (x-7) ^3

factors are

(x+7) and (x-7)

see the x+7 appears 2 times since it is to the 2nd power, means multiplicity 2

x-7 appears 3 times since to 3rd power, means multipilcty 3

but the roots are negative

so

(x - (-7)) ^2 and (x-7) ^3

roots are - 7 multiplicty 2 and 7 multiplicty 3

A is answer