4/30 Alg2: Review of Zeros and Theorems of Polynomials

Zeros of Polynomials and Theorems About Polynomials

Let's review 3-5 and 3-6 for our test next week!

Multiple Choice

Which of the following is NOT a zero of the polynomial?

• (0, 0)

• (-3, 0)

• (1, 0)

• (4, 0)

Multiple Choice

Which of the following is NOT a zero of the polynomial?

 $f\left(x\right)=x\left(x-1\right)\left(x+7\right)$  

• x = 0

• x = -1

• x = 1 

• x = -7

Multiple Choice

Which of the following is NOT a zero of the polynomial?

 $f\left(x\right)=\left(x-5\right)\left(x+2\right)\left(x+6\right)$  

• x = 0

• x = -1

• x = 1 

• x = -7

Multiple Choice

Describe the behavior of the graph of the function at its zero x = 1.

 $f\left(x\right)=x\left(x+4\right)\left(x-1\right)^4$  

• The multiplicity of x =1 is 4, so the function crosses the x‑axis.

• The multiplicity of x =1 is 4, so the graph has a turning point on the x-axis.

Multiple Choice

Describe the behavior of the graph of the function at its zero x = 1.

 $f\left(x\right)=\left(x^2+9\right)\left(x-1\right)^5\left(x+2\right)^2$  

• The multiplicity of x =1 is 5, so the function crosses the x‑axis.

• The multiplicity of x =1 is 5, so the graph has a turning point on the x-axis.

Multiple Choice

This function has 3 zeros in the set of complex numbers, but it only looks like it has a zero at x = 2. How can this be?

• x = 2 is the real solution, there are 2 other complex solutions.

• The first option.

• The second option.

• The third option.

Multiple Choice

Use the attachment to help you.

According to the Rational Root Theorem, which of the following is NOT a possible solution to the polynomial?

 $P\left(x\right)=4x^3-7x+5$  

•  $5$  

•  $-\frac{1}{2}$  

•  $\frac{2}{3}$  

•  $\frac{5}{4}$  

Multiple Choice

Use the attachment to help you.

According to the Rational Root Theorem, which of the following is NOT a possible solution to the polynomial?

 $P\left(x\right)=7x^4-x^2+5x-6$  

•  $6$  

•  $-\frac{1}{7}$  

•  $\frac{2}{7}$  

•  $\frac{5}{4}$  

Multiple Choice

According to the Fundamental Theorem of Algebra, how many roots exist for the following polynomial?


 $P\left(x\right)=5x^7-6x^3+17x^2-19$  

• 5

• 7

• 19

• None

Complete your exit ticket and you are finished for the day!