Question

2. Name the multiplicity of each zero for the following polynomialType your answer with spaces no commas*f (x) = –2x(3x + 1)2(x + 7)7

Answer 1

x = 0 has multiplicity 1.

x = -1/3 has multiplicity 2

x = -7 has multiplicity 7

Explanation:

We are given the following polynomial:

`f(x)=-2x(3x+1)^2(x+7)^7`

The roots(zeros) are:

Values of x for which:

2x = 0, 3x + 1 = 0 or x + 7 = 0

2x = 0

x = 0/2

x = 0

3x + 1 = 0

3x = -1

x = -1/3

x+7 = 0

x = -7

Their multiplicities are:

The exponent of each term.

2x is not elevated to any value.It's respective root is x = 0, so x = 0 has multiplicity 1.

(3x+1) has exponent 2. So x = -1/3 has multiplicity 2.

(x+7) has exponent 7. So x = -7 has multiplicity 7