Question

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

Answer 1

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