Integrated II Homework 21: Polynomial Terms

Integrated II Homework 21: Polynomial Terms

Before you begin this, be sure you have the new packet to follow along as this is the first part of the first lesson.

You will see example problems and then do problems of your own after seeing the content​

Read through the basic aspects of polynomials on page 2 of the packet:

• *Names of polygons according to number of terms

• *Degree of polygon

• *Converting a polygon to Standard Form

• *Identifying the Lead Coefficient​

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For the following examples, I will name each polynomial by its number of terms and state its degree

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These are the practice in your packet so fill in the correct answers as you go!​

a) 8ab - 2c

This is a binomial because it has 2 terms (8ab and -2c)

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​8ab has a degree of 2 (8a¹ b¹ ) and 2x has a degree of 1 (2x¹ )

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So the polynomial has a degree of 2​ since the highest degree term = the degree of the polynomial

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ANSWER: binomial of degree 2​

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b) -11.25

This is a monomial because it has just 1 term

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-11.25 has a degree of 0 (-11.25x⁰ )

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So the polynomial has a degree of 0

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ANSWER: monomial of degree 0

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c) 2x^-2 + 3xy

The -2 exponent means that the first term is actually 2 divided by x²​

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ANSWER: this is not a polynomial because the first term is a division problem and not multiplication. Basically if a term has a negative exponent, it is not a polynomial

d) 2m² + 2mn - n²

This is a trinomial because it has just 3 terms (2m² and 2mn and -n² )

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All three terms have a degree of 2​

So the polynomial has a degree of 2

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ANSWER: trinomial of degree 2

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Multiple Choice

Which two statement are correct if telling the name and degree of the polynomial

3z^-2 ?

• This is a monomial of degree -2

• This is a monomial of degree 3

• This is not a polynomial

• This is a polynomial of degree -6

If you missed it, look back at example problem c: If an expression has a negative exponent, it cannot be a polynomial

Multiple Select

Which two statements are correct regarding the polynomial:

2x³ + x - 12

• This is a trinomial

• This is a binomial

• The degree is 3

• The degree is 2

2x³ and x and -12 are all terms so it is a trinomial (3 terms)

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The highest degree is 3 for 2x³​

Multiple Select

Which two statements are correct regarding the polynomial

9x - 2

• This is a binomial

• This is a monomial

• The degree is 1

• The degree is 0

9x and -2 are terms so it is a binomial

(2 terms)

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The highest degree is 1 for 9x¹​

Polynomials in Standard Form

​Listed with highest degree first and powers decreasing, left to right. If multiple variables, use the variable that is alphabetically first

Some text here about the topic of discussion

Lead Coefficient

​A coefficient is the number in the front of a term. The "lead coefficient" is the number in the front of the first term of a polynomial after it has been written in standard form

Some text here about the topic of discussion

Examples: Rewriting in standard form and stating the lead coefficient

These are the practice in your packet so fill in the correct answers as you go!​​

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a) 5x² - 2 + 3x = +5x² - 2 + 3x¹

highest power is 2 so 5x² is the first term

next highest power is 1 so +3x is the next term​

-2 doesn't have a power, so it is last​

thus the standard form= 5x² + 3x - 2

The lead coefficient is 5​

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b) 8y + 7y³ = +8y¹ + 7y³

the highest power is 3 so 7y³ is the first term

the next highest power is 1 so +8y is the next term​

thus standard form = 7y³ + 8y

The lead coefficient is 7​

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c) 4 - 3c - 5c² = +4 - 3c¹ - 5c²

the highest power is 2 so -5c² is the first term

the next highest power is 1 so -3c is the next term​

+4 doesn't have a power so it is the last term​

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thus standard form = -5c² - 3c + 4

The lead coefficient is -5​

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d) 11xy + x² - 2y² = +11x¹y¹ + 1x² - 2y²

the highest power is 2 and x is before y in the alphabet so x² is the first term

the next highest power for x is 1 so +11xy is the next term

this leaves -2y² as the last term​

thus standard form = x² + 11xy - 2y²

The lead coefficient is 1​

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Now your questions: Rewrite the following polynomial in standard form:

4x + 12 + 2x³ - 3x²

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answer choices are on the next slide but don't move to that until you are ready!​

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Multiple Select

Which two statements are correct for the polynomial?

4x + 12 + 2x³ - 3x²

• Standard form is 12 + 4x - 3x² + 2x³

• Standard form is 2x³ - 3x² + 4x + 12

• The lead coefficient is 2

• The lead coefficient is 4

Rewrite the following polynomial in standard form:

5b - 10b² + 35 - b³

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answer choices are on the next slide but don't move to that until you are ready!​

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Multiple Select

Which two statements are correct for the polynomial?

5b - 10b² + 35 - b³

• Standard Form is

  b³ - 10b² - 5b + 35

• Standard Form is

  -b³ - 10b² + 5b + 35

• The lead coefficient is -1

• The lead coefficient is 1

Rewrite the following polynomial in standard form:

2ab + 3b² - 5a²

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answer choices are on the next slide but don't move to that until you are ready!​

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Multiple Select

Which two statements are correct for the polynomial?

2ab + 3b² - 5a²

• Standard Form is 3b² - 5b² + 2ab

• Standard Form is

  -5a² + 2ab + 3b²

• The Lead Coefficient is 3

• The Lead coefficient is -5

Rewrite the following polynomial in standard form:

84m + 3m² - m⁵

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answer choices are on the next slide but don't move to that until you are ready!​

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Multiple Select

Which two statements are correct for the polynomial?

84m + 3m² - m⁵

• Standard Form is m⁵ + 3m² + 84m

• Standard Form is

  - m⁵ + 3m² + 84m

• The Lead Coefficient is 1

• The Lead Coefficient is -1

The End!

You may choose to ReStart this and do it again if you want to improve your score and learn the material a little bit better :)