Multiplicities

Multiplicities

by Melissa Mitchell

Multiple Choice

What is the degree of the polynomial?

$$g\left(x\right)=\left(x-4\right)^2\left(x+7\right)^3$$  

• 6

• 5

• 1

• 9

Multiple Choice

What is the degree of the polynomial?

$$m\left(x\right)=x\left(x+5\right)\left(x-6\right)$$  

• 3

• 2

• 9

• 6

Multiple Choice

What is the degree of the polynomial?

$$f(x)=(x-3)^4(x+1)^7$$  

• 3

• 28

• 11

• 12

Multiple Choice

What are the zeros with multiplicities?

$$g(x)=(x+4)^2(x+8)^3(x-5)$$  

• -4 multiplicity 1, -8 multiplicity 1, 5 multiplicity 3

• 4 multiplicity 2, 8 multiplicity 3, -5 multiplicity 1

• 4 multiplicity 3, 8 multiplicity 2, -5 multiplicity 1

• -4 multiplicity 2, -8 multiplicity 3, 5 multiplicity 1

Multiple Choice

What are the zeroes with multiplicity?

$$k(x)=(x+2)^{10}(x-12)^9$$  

• -2 multiplicity 9, 12 multiplicity 10

• -2 multiplicity 10, 12 multiplicity 9

• 2 multiplicity 10, -12 multiplicity 9

• 2 multiplicity 9, -12 multiplicity 10

Multiple Choice

What are the zeros with multiplicities?

$$h(x)=(x-2)(x-5)(x+6)$$  

• 2 multiplicity 1, 5 multiplicity 1, 6 multiplicity 1

• -2 multiplicity 1, -5 multiplicity 1, -6 multiplicity 1

• 2 multiplicity 1, 5 multiplicity 1, -6 multiplicity 1

• -2 multiplicity 1, -5 multiplicity 1, 6 multiplicity 1

Multiple Choice

Find the correct statement about the zeros.

• −5 is a zero with multiplicity 1

• −5 is a zero with multiplicity 2

• −2 is a zero with multiplicity 1

• 2 is a zero with multiplicity 2

Multiple Choice

Which polynomial has 3 factors of (x – 1) and two factors of (x + 7)?

• $$b\left(x\right)=\left(x-1\right)^3\left(x+7\right)^2$$

• $$b\left(x\right)=\left(x-1\right)^2\left(x+7\right)^3$$

• $$b\left(x\right)=\left(x+1\right)^3\left(x-7\right)^2$$

• $$b\left(x\right)=\left(x+1\right)^2\left(x-7\right)^3$$

Multiple Choice

What is the equation of a polynomial with 5 factors of (x – 5), 6 factors of (x + 5), and 4 factors of (x + 4)?

• $$f\left(x\right)=\left(x-5\right)^5\left(x+5\right)^6\left(x+4\right)^4$$  

• $$f\left(x\right)=\left(x-5\right)^6\left(x+5\right)^5\left(x+4\right)^4$$  

• $$f\left(x\right)=\left(x+5\right)^5\left(x-5\right)^6\left(x-4\right)^4$$  

• $$f\left(x\right)=\left(x-5\right)^4\left(x+5\right)^5\left(x-4\right)^6$$  

Multiple Select

Which of the following are words that mean SOLUTIONS? Choose ALL of the possible answers.

• Zeroes

• Roots

• X-intercepts

• Y-intercepts