Algebra 2- 6.3/6.4 Review

6.3-6.4 Review

Algebra II

Multiple Choice

x³-3x²-10x+24 ÷ x+3

• x²-7x+5

• x-8

• x²-6x+8

• x+9

Multiple Choice

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9

• 3x² - 3x + 8 - 9/x+1

• 3x² + 3x + 8 + 7/x+1

• 3x³ + 3x² + 8x + 7

Multiple Choice

(2x³ + 5x² + 9) ÷ (x + 3)

• 2x² - x + 3

• 2x³ - x² + 3x

• 2x² + 11x + 33 + 108/x+3

• 2x² - 5x + 12

Let's analyze some remainders!

Let's start by using synthetic division together.

Think to yourself. What is the polynomial represented by this synthetic division? (You will answer on the next slide)

Multiple Choice

Evaluate P(-5).

• 4

• 25

• -17

• -29

Multiple Choice

Divide using synthetic division

  $$\left(x^3-8x^2-29x+180\right)\div\left(x-10\right)$$  

What is the remainder?

• 0

• 90

• 180

• -90

To solve a polynomial means to do all these things:

• find the solutions

• find the zeroes

• find the roots

• find the x-intercepts

Multiple Choice

Factor x³ - 1000 using Difference of Cubes

• (x + 10)(x² - 10x + 100)

• (x - 10)(x² + 10x + 100)

• (x - 1)(x² + 1x + 1)

• (x - 5)(x² + 5x + 25)

Steps for solving a polynomial using factoring:

1. Factor completely (check each factor)

2. Set each factor to zero

3. Solve each factor for the variable

4. Write the solutions for the variable

Multiple Select

Solve the following polynomial.         $$x^4+16=8x^2$$  (select all that apply)

• $$x=0$$  

• $$x=\pm2$$  

• $$x=\pm4$$  

• $$x=8$$  

• $$x=1$$  

Multiple Select

Find the zeros. $$g\left(x\right)=3x^3-15x^2-72x$$   (select all that apply)

• $$x=-3$$  

• $$x=8$$  

• $$x=-7$$  

• $$x=0$$  

• $$x=3$$  

Multiple Select

Find the zeros:                 (select all that apply)                 

$$f\left(x\right)=5w^3-125w$$  

• $$w=5$$  

• $$w=-5$$  

• $$w=0$$  

• $$w=25$$  

• $$w=5i$$