Math problem

Question

Consider the polynomial p(x)=-2(x-4)^3(3x+3)(2x-10)(x+1)^5. Determine the zeros of p(x) and their multiplicities.

Answer 1

The multiplicity is the number of times a zero appears.  The exponent of the zero's factor represents the multiplicity.

 

Set these factors equal to zero: 

 

(x - 4)³ 

 

(3x + 3) 

 

(2x - 10)

 

(x + 1)⁵

 

 

Using these factors, we can easily get our zeros and the multiplicities.

 

The zero x=4 has multiplicity of 3.

The zero x=-1 has a multiplicity of 1.

The zero x=5 has a multiplicity of 1.

The zero x=-1 has a multiplicity of 5.