A.2 Naming polynomials

Introduction to Polynomials

Target: Identify the degree and lead coefficient of a given polynomial.

A math expression containing two or more algebraic terms

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Ex: 4x⁵​ + 2x⁴ - 3x³ + 8x² + 7x - 10

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​Polynomials Definition

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Simply: rearrange the terms of the polynomial so the largest exponent is first, and the smallest exponent is last

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​10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 -2 - 1

​Let's talk descending order

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​STANDARD FORM of a POLYNOMIAL

all of the terms are in order from highest degree to the lowest degree.

​EXAMPLE

Write in STANDARD FORM

​5y² + w⁴ + w⁷ - q³ + 2y - 10

Multiple Choice

Which answer properly places the polynomial in the correct descending order?

$$6x^2+7x^4+5x^3+15-8x$$  

• $$7x^4-8x+6x^2-5x^3+15$$  

• $$5x^3+7x^4-8x+6x^2+15$$  

• $$15-8x+7x^4+6x^2+5x^3$$  

• $$7x^4+5x^3+6x^2-8x+15$$  

Multiple Choice

Which answer properly places the polynomial in the correct descending order?

$$9x^5-3x^2+8x-18$$  

• $$9x^5-3x^2+8x-18$$  

• $$-3x^2+8x-18+9x^5$$   

•   $$-18+9x^5-3x^2+8x$$  

•   $$-18+9x^5+8x-3x^2$$  

The degree of a polynomial is determined by the LARGEST exponent.

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This is why its beneficial to put into descending order.​

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​Some text here about the topic of discussion.

​Degrees of Polynomials

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Multiple Choice

What is the degree of the polynomial

$$7x^4-8x^6+2x^2-10$$  

• 4

• 6

• 2

• 0

Multiple Choice

What is the degree of the polynomial

$$10x^3-7x^2+9x^5-x^8+7$$  

• 3

• 2

• 5

• 8

Based on the degree of the polynomial, we can assign a name to that polynomial

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Names are shown to the left

​Names of Polynomials

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Multiple Choice

What is the name of the polynomial shown?

$$7x^3+5x^2-8x+10$$  

• Cubic

• Quartic

• Quadratic

• Zero

Multiple Choice

What is the name of the polynomial shown?

$$-3x^5+8x^2-10+7x-4x^3$$  

• Cubic

• 7th degree Polynomial

• Quintic

• Zero

The number of terms will create a classification for each polynomial

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ex: 3 terms = trinomial​

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​Naming Polynomials based on the number of terms

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Multiple Choice

Name the following polynomial

$$5x^2+2x-10$$  

• Monomial

• Binomial

• Trinomial

• Polynomial with degree of 0

Multiple Choice

Name the following polynomial

$$-3x^4+6x$$  

• Monomial

• Binomial

• Trinomial

• Polynomial with degree of 0

Multiple Choice

Name the following polynomial

$$7x^3y^2$$  

• Monomial

• Binomial

• Trinomial

• Polynomial with degree of 0

Multiple Choice

Name the polynomial and the number of terms

$$8x^2+6x-16$$  

• Trinomial with 3 terms

• Binomial with 2 terms

• Polynomial with 4 terms

• Monomial with 2 terms

Multiple Choice

Name the polynomial and the number of terms

$$-12x^4$$   

• Trinomial with 3 terms

• Binomial with 2 terms

• Polynomial with 4 terms

• Monomial with 1 term

Multiple Choice

Name the polynomial by degrees and number of terms

$$5x^4+8x^2-10x$$  

• Polynomial, 4 degrees, 3 terms

• Binomial, 4 degrees, 2 terms

• Monomial, 4 degrees, 1 term

• Trinomial, 4 degrees, 3 terms

Multiple Choice

Name the polynomial by degrees and number of terms

$$10x^3+7x^2$$   

• Polynomial, 3 degrees, 2 terms

• Binomial, 4 degrees, 2 terms

• Trinomial, 4 degrees, 2 terms

• Monomial, 4 degrees, 1 term

Multiple Choice

Write the following polynomial in descending order in terms of b

$$b^3-a^2b+4ab^4-10a$$  

• $$4ab^4+b^3-a^2b-10a$$  

• $$-10a+4ab^4-a^2b+b^3$$  

• $$-a^2b-10a+4ab^4+b^3$$  

Multiple Select

Choose all the binomial expressions.

• -5x + 12

• 2x²

• 2y² - 2y + 2

• 19 - 7y

• 3x³ - 3

Multiple Choice

Name the polynomial by its degree.

$$3x^2+7x-8$$  

• constant

• linear

• quadratic

• cubic

Multiple Select

Chose all the descriptions that describe the polynomial.

$$-2x^2-7$$  

• trinomial

• linear

• quadratic

• binomial

• monomial

Naming Polynomials

This isn't too important to memorize, but we will use some of this vocabulary such as binomial and trinomial in the future.

The degree is the highest exponent in the polynomial.

Multiple Choice

Classify by number of terms:

3x² – 8x + 1

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
9x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by number of terms:

3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify the polynomial:

$$14x^3+x^2-x+2$$  

• Quadratic trinomial

• Triad 

• Cubic 

• Fourth degree polynomial

Multiple Choice

Write the polynomial in standard form:

$$7x^3-11x+x^5-2$$  

• $$-11x+7x^3-2+x^5$$  

• $$x^5+7x^3-11x-2$$  

• $$7x^3-11x+x^5-2$$  

• $$18x^5-2$$