Algebra II 6.

Question

Find the zeros of the polynomial and state the multiplicity of each zero.
f(x) = 3(x + 6)2(x - 6)3
Question 6 options:

1) x = -6, multiplicity 2; x = 6, multiplicity 3

2) x = -6, multiplicity 3; x = 6, multiplicity 2

3) x = 4, multiplicity 1; x = 6, multiplicity 1; x = -6, multiplicity 1

4) x = 4, multiplicity 1; x = -6, multiplicity 3; x = 6, multiplicity 3

Answer 1

Hi Carrie,

 

Find the zeros of the polynomial and state the multiplicity of each zero.
f(x) = 3(x + 6)²(x - 6)³
Question 6 options:

1) x = -6, multiplicity 2; x = 6, multiplicity 3

2) x = -6, multiplicity 3; x = 6, multiplicity 2

3) x = 4, multiplicity 1; x = 6, multiplicity 1; x = -6, multiplicity 1

4) x = 4, multiplicity 1; x = -6, multiplicity 3; x = 6, multiplicity 3

 

 

Since the factor (x + 6)  is squared, then its multiplicity is 2.

Solve x+6=0

x=-6

 

Since the factor (x - 6) is cubed, then its multiplicity is 3

Solve x-6=0

x=6

 

ANSWER: x=-6 multiplicity is 2;  x=6 multiplicity is 3.   (Option #1)

 

 

Answer 2

Assuming that what you mean in the question is f(x) = 3(x+6)2(x-6)3;

 

Equating the function to 0;  3(x+6)²(x-6)³ = 0; you can now remove some constant factor;  (x+6)²(x-6)³ = 0

 

From there, the factors are simply (x+6) two times and (x-6) three times, equating those again independently to 0, you will get x = -6 two times and x = 6 three times.