Module 10: Lesson 1: Polynomials

Module 10: Lesson 1: Polynomials

Presented by: Mr. Carozza

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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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

$$b^3-a^2b+4ab^4-10a$$  

• $$4ab^4+b^3-a^2b-10a$$  

• $$-10a+4ab^4-a^2b+b^3$$  

• $$-a^2b-10a+4ab^4+b^3$$