Unit 4 Review (Algebra 2)

​Unit 4 Review

Algebra 2​

​Sections in Unit 4

• ​4.1 Intro to Polynomials

• 4.2 Polynomial Division

• 4.3 Finding roots given a rational root(s)

• 4.4 Finding roots given an irrational/imaginary root(s)

• 4.5 Rational Roots Theorem (p/q list)

• 4.6 Finding roots using Desmos

• 4.7 Finding polynomial given roots

• 4.8 Story problems​

Multiple Choice

Name the type of function:

• Linear (deg1)

• Quadratic (deg2)

• Cubic (deg3)

• Quartic (deg4)

Multiple Choice

How many solutions are there for the function?

• None

• 3 real

• 1 imaginary, 2 real

• 2 imaginary, 1 real

Multiple Choice

Is the leading coefficient of this polynomial positive or negative?

• Positive

• Negative

Fill in the Blanks

What is the degree of the following function?

$f\left(x\right)=-7x^5-x^4+2x+1$  

Multiple Choice

For the following polynomial, would the end behavior of the graph on the RIGHT side be up or down?

$$f\left(x\right)=-\frac{1}{2}x^6+7x^5-4x^3+9$$  

• Up

• Down

Fill in the Blanks

Find the REMAINDER when dividing $\left(x^3+4x^2-7x+1\right)\div\left(x+3\right)$  .

Multiple Choice

Is $$\left(x+3\right)$$  a factor of $$2x^3+7x^2-9$$  ? If so, select the other factors.

• (x+3)(x-3)

• (2x-1)(x+1)

• (x-3)(2x+1)

• (x-1)(2x+3)

• It's not a factor.

Multiple Choice

Which of these is NOT a possible rational root of $$f\left(x\right)=6x^3+x^2-7x+9?$$  

Hint: Make a p/q list.

• -9

• 9/4

• 1/3

• -1

• 3/2

Multiple Choice

Bobby solved the polynomial $$f\left(x\right)=x^6+x^3-7x^2-8x+1$$   and got 3 real solutions and 3 imaginary solutions. Is this possible? Why?

• Yes, because the 3 real and 3 imaginary make 6 total.

• Yes, because there are 5 terms in the polynomial.

• No, because imaginary solutions always come in conjugate pairs.

• No, because the only possible rational solutions are 1 & -1.

Multiple Choice

Find the other roots of the function, $$f\left(x\right)=x^3+2x^2-5x-6$$  , given that one of its roots is $$x=-3$$  .

• x = 2, -1

• x = 1, -2

• x = 3i, -3i

• x = 7i, -7i

• x = 4, 1/2

Multiple Choice

Find the other roots of the function, $$f\left(x\right)=x^3-5x^2-3x+15$$  , given that one of its roots is $$x=-\ \sqrt[\ ]{3}$$  .

• $$x=-1,\ 3$$  

• $$x=-1,\ -3$$  

• $$x=\ \sqrt[]{3},\ 5$$  

• $$x=\ \sqrt[]{3},\ -5$$  

• $$x\ =\ \sqrt[]{3},\ 7$$  

Multiple Choice

Using the Rational Roots Theorem (p/q) and/or Desmos, find all roots for the function: $$f\left(x\right)=2x^3-3x^2+8x-12$$  .

• x = 3/2, 2i, -2i

• x = 1/3, 4i, -4i

• x = 3/4 , 2i, -2i

• x = 6/5 , 4i, -4i

Multiple Choice

A videogame company models profit using the following function, $$p\left(x\right)=-2x^3+9x^2+11x-30$$  , where the number of games produced (x) and profit (p(x)) are both in millions.

Between what values of games does the company make a profit? Also, what is the maximum profit they can make?

Use Desmos to create a graph.

• 10 million to 15 million games ; around $92 million

• 1 million to 2 million games ; around $17 million

• 1.5 million to 5 million games ; around $33 million

​That's it!

• ​Use this presentation as a simulation of your coming test!

• You can retry the practice version in Modules as much as you want!

• If something went poorly, address it soon!​