5.1-5.5 Review (AA2)

5.1-5.5 Review (AA2)

Sections / Topics in 5.1-5.5

• 5.1 Operations with Polynomials

• 5.2 Polynomial Division (Synthetic and Long)

• 5.3 Polynomials as Functions

• 5.4 Graphs of Polynomial Functions

• 5.5 Factoring and Solving Polynomial Equations

5.1 Questions

The following are exercises within 5.1. Be prepared to see these kinds in the assessment!

Multiple Choice

Simplify

 $\left(4r^2+3r-1\right)-\left(3r^2-5r+4\right)$  .

•  $7r^2+3r-5$  

•  $r^2+8r-5$  

•  $r^2-2r+5$  

Multiple Choice

Simplify

 $\left(3x^3\right)^2\ \ \left(-x^3\right)$  

•  $9x^6$  

•  $-3x^8$  

•  $-9x^9$  

Multiple Choice

Simplify

 $\frac{14x^4y}{2x^3y^5}$  

•  $7xy$  

•  $\frac{7x}{y^4}$  

•  $\frac{7x}{y}$  

5.2 Questions

Be prepared to see these kinds on the assessment!

Multiple Choice

Divide

 $\frac{6y^3+13y^2-10y-24}{y+2}$  with either synthetic or long division.

•  $6y^2+y-12$  

•  $6y^2-y+12\ -\frac{4}{y+2}$  

•  $y^2-6y+2$  

Multiple Select

If you were to synthetically divide

 $\frac{a^4+5a^3+2a^2-6a+4}{a+2}$  which of the following are true?

• 2 would go in the little box

• -2 would go in the little box

• You add the columns

• You subtract the columns

• You bring the first coefficient straight down

5.3 Questions

Be ready to see these topics in the assessment!

Multiple Choice

Select the degree and leading coefficient of

 $f\left(x\right)=3x^3-7x^2+x-9$  

• Degree: 3 
  Leading Coefficient: 3

• Degree: 2
  Leading Coefficient: 3

• Degree: 2
  Leading Coefficient: -7

Multiple Choice

Find f(-2), if

 $f\left(x\right)=2x^2-x+7$  

• 13

• 1

• 17

• 7

5.4 Questions

These may be on the assessment!

Multiple Select

Select the following that are TRUE.

• The function has 2 relative maxima.

• The function has 2 relative minima.

• The function has 3 relative maxima.

• The function has 3 relative minima.

• The function is odd.

Multiple Choice

How many real solutions does the graph have?

• 4

• 3

• 5

5.5 Questions

These types could be on the assessment...

Multiple Choice

What would be the method to factor the following polynomial?

 $6ay+4by-2cy+3az+2bz-cz$  

• GCF

• Quadratic Trinomial

• Grouping

Multiple Choice

Choose the proper factorization for the following sum of cubes.

 $p^3+27$  

•  $\left(p+3\right)\left(p^2-3p+9\right)$  

•  $\left(p+3\right)\left(p-3\right)$  

•  $\left(p-3\right)\left(p^2+3p+9\right)$  

Multiple Choice

I'm solving an equation and I get to something like this:

 $\left(x-2\right)\left(x^2+3x+8\right)=0$  
The second factor can't be factored or broken down any more, so what should I do to solve for x?

• It can't be factored or solved.

• Use the quadratic formula  for the second factor since it's second degree.

• Check for errors because quadratic trinomials always factor.

Multiple Choice

Finish the following and solve the polynomial equation.

 $x^3-x^2-9x+9=0$  

 $\left(x^2-9\right)\left(x-1\right)=0$  

 $x^2-9=0$    or    $x-1=0$   

•  $x=\pm3,\ -1$  

•  $x=\pm3,\ 1$  

•  $x=9,\ 1$  

•  $x=\ -9,\ -1$  

That's all!

Be sure to review old notes and homework if you weren't confident with these topics.