Lesson: Polynomial Operations Review

​Lesson: Polynomial Operations Review

​Standard Form

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11

• 9x³ + 8x² - 3x - 11

• 8x² + 9x³ -11 - 3x

• -11 - 3x + 8x² + 9x³

Multiple Select

Which of these is in Standard Form?

• $$4x^2+12x-13x^3$$  

• $$5-3x$$  

• $$2x^4-12x^2+5x-9$$  

• $$5x^5+4x^{\text{4}}+12x^3-23x+15$$  

​- Name of Author

" Replace this with a quote, words full of wisdom that someone important said and can inspire the reader. " 

Multiple Choice

Identify the degree of the monomial:
8a³

• 8

• 1

• 3

• 11

Multiple Choice

A polynomial that has two terms is a:

• polynomial

• monomial

• binomial

Classify by number of terms:

You probably recognize these!

Study the chart ====>

Multiple Choice

Classify by number of terms:

x² + 4x -8

• binomial

• trinomial

• monomial

• polynomial

Multiple Choice

Classify by number of terms:

2n³

• Monomial

• Binomial

• Trinomial

• Polynomial

Leading Coefficient & Constant Term

Look at the chart ===>

The leading coefficient is the number in front of the highest degree variable.

The constant is the number without a variable.

Write in standard form 1st to make these easy to identify!

The CONSTANT here is 0!

Multiple Choice

Put in standard form first. Then, give the Leading Coefficient (LC) and the Constant:

$$3x+5x^4-9$$  

• LC = 3;  
  
  constant = 9

• LC = 5; 
  
  constant = 9
  

• LC = 5; 
  
  constant = -9

• LC = 4; 
  
  constant = -9

Multiple Choice

What is the leading coefficient (LC) and the constant?

f(x)=5x²+3x³-2x

• LC: 5

  Constant: 0

• LC: 3

  Constant: -2

• LC: -2

  Constant: 3

• LC: 5

  Constant: -2

Like terms have:

Same variables with same exponents!

You can add like terms vertically!

Some find this an easier way to get their answer.

Like-terms are written under each other and then added down.

Multiple Choice

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1
• -2x² - 11x -4
• 2x² + 5x -7
• -2x² + 11x -4

Subtracting Polynomials

Distribute the negative and rewrite the 2nd polynomial.

Then lose the parentheses and combine like terms.

You can also line them up vertically and add down!

DISTRIBUTING THE (-) IS THE SAME AS MULTIPLYING BY -1 !

Multiple Choice

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8
• 2x² + 5x - 7
• -x² -6x + 8
• -2x² + 11x - 4

Multiplying

Polynomials

Here are the types of problems you'll need to be able to answer

To multiply by a MONOMIAL, just distribute

Binomial x Binomial

Distribute twice using FOIL or a

BOX. Here is the Box method ==>

Put the terms on the outside of a box and multiply. Add like terms on the diagonal.

You might have done this in Biology with Punnett Squares!

Binomial x Trinomial

Distribute each term in one expression.

Draw a 2 x 3 box to use the Box method.

Remember to write your answer in standard form!

Multiple Choice

Multiply: 2x³(x²−2x − 3)

• 2x⁶- 4x³ - 6x³

• 2x⁵−4x⁴ − 6x³

• -2x⁵−4x⁴ − 6x³

• -2x⁶−4x³ − 6x³

Multiple Choice

Multiply: (x − 3)(6x − 2)

• 6x² − 20x + 6

• 6x² + 20x - 6

• 6x² +6

• 6x + 6

Multiple Choice

Multiply: (4a + 2)(6a² − a + 2)

• 24a³ + 16a² + 6a + 4

• 24a³ + 8a² + 10a + 4

• 24a³ + 8a² + 6a + 4

• 24a³ - 8a² - 6a + 4