College Prep Math Final Exam Review #1 Polynomials

College Prep Math Final Exam Review #1 Polynomials

Today we will be reviewing adding, subtracting and multiplying polynomials.

Adding and Subtracting Polynomials

• Step 1 (Subtraction) Distribute the negative to all terms after the negative sign

• Step 2 (Both) Rewrite the polynomials in "degree order" putting the highest exponents first, etc (x⁴...x³... x² ... x... #) (When you move the terms, be sure to move the sign with the term.)

• Step 3 Combine like terms by adding the coefficients (3x + 4x = 7x)

Multiple Choice

Add:
(3x² - 3x + 2) + (x² - 2x + 1)

• A
  4x³-2x²+2
• B
  4x² - 5x + 3
• C
  -2x³+2x+2
• D
  4x³-2x²-2

Multiple Choice

Add or subtract to simplify.
 $\left(5x+x^2-4\right)-\left(4x-x^2+6\right)$  

• 2x² + x + 2 

• x + 2

• 2x² + x - 10 

• x - 10 

Multiple Choice

Subtract:

When (-3x² + 2x - 1) is subtracted from (3x² - 3x + 2), what will be the difference?

**Remember my example that I am from Michigan, so Michigan is where I started. (What comes after "from" is where you start.)

• A

  0x² - x + 1

• B

  6x² - x + 1

• C

  6x² - 5x + 3

• D

  6x² + 5x + 3

Apply yourself.

Here are some reminders:

*Perimeter means to add all the sides.

*If you have two areas and you are trying to find the missing space you can subtract the two areas. Big one minus small one.

Multiple Choice

The total area of the playground, the larger rectangle, is 
16x² − 5x + 2. The area of the play area, the smaller rectangle, is 10x² + 3x − 1. Write an expression to represent the area of the sidewalk.

• 6x² − 8x + 3
• 16x² − 8x + 3
• 16x² − 2x + 1

Multiple Choice

What is the perimeter of the rectangle?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

Multiple Choice

What is the perimeter of the triangle shown?

• 9r²+r-5
• 9r⁴+r²-4
• 9r²-r+4
• 9r²+r-4

Multiply Polynomials

If you need a reminder, listen to the instructions.

Remember that each term in the first group needs to get distributed (multiplied) to each term in the second group.

(x + 3)(x - 2) =

x(x) + x(-2) + 3(x) + 3(-2) =

x² - 2x + 3x - 6 =

x² + x - 6

Multiple Choice

Multiply the following together:

(3x - 2)(6x + 1)

• 18x² - 2

• 9x² -9x -2

• 18x² -9x -2

• 3x² -12x

Multiple Choice

Multiply the following together:

(2x + 3)(x² + 4x + 1)

• 2x³ + 8x² +2x

• 3x² + 12x +3

• 2x³ +11x² +14x +3

• 2x³ + 12x +3

Apply yourself.

Reminders:

Area of a rectangle = length times width

Area of a triangle = 1/2 (base times height)

Multiple Choice

Find the area of a rectangle with length (x-5) and width (3x+1).

• 3x²+16x-5
• 3x²-14x+5
• 3x²-14x-5

Multiple Choice

What is the Area?

• 2x² - 3x - 18 inches²
• 2x² + 3x + 18 inches²
• 2x² + 9x - 18 inches²
• 2x² - 9x - 18 inches²

Multiple Choice

What is the area of a triangle whose base is (x + 2) and whose height is (8x - 10)?

• 8x² - 6x - 12

• 4x² - 6x -10

• 4x² + 3x - 10

• 8x² + 6x - 20