Lesson: Introduction to Polynomials

Multiple Select

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Introduction to Polynomials

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

Math Response

Combine Like Terms: 3x² - 4 + 2x - 5x² + 12

Type answer here

Correct Answer: -2x^2+2x+8

Deg^°

Rad

​TERM

- a number, a variable, or the product of a number and variable(s)

​EXAMPLES

​​poly- "many" -nomial "term" Term(s) whose exponents are whole numbers, and are separated by a "+" or a "-"

​POLYNOMIAL

​​x + 3

​​x² - 4x - 9

​9​x³ + 5x² - 3x + 12

​How many terms does each polynomial have?

Math Response

How many terms does the polynomial have?

$$2ab^2-4c+6d^3-12ef\ +\ 101$$  

Type answer here

Correct Answer: 5

Deg^°

Rad

​STANDARD FORM of a POLYNOMIAL

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

​EXAMPLE

Write in STANDARD FORM

​5y² + w⁴ + w⁷ - q³ + 2y - 10

Reorder

Rewrite $$2x^2+9-5x^3+3x^4-8x$$ in standard form.

• $$+3x^4$$

• $$-5x^3$$

• $$+2x^2$$

• $$-8x$$

• $$+9$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

​DEGREE OF A POLYNOMIAL

​EXAMPLES

​3x² + 9x - 4

​x² - 8x⁵ + 7

​y⁵z⁴ + w²x³ + 2xy - 10

​the degree is ___

​the degree is ___

​the degree is ___

the highest degree of its monomials with non-zero coefficients.

Math Response

What is the degree of the polynomial?

$$a^3b^3+c^4d-x^3y^2$$  

Type answer here

Correct Answer: 6

Deg^°

Rad

​LEAD COEFFICIENT

the coefficient of the first term when the polynomial is written in standard form.

​EXAMPLE

What is the lead coefficient?

​-9x³ + 3x - 6x⁴ + 22

Math Response

What is the lead coefficient of the polynomial?

$$-4a^3+19a^4-a+12a^6+103$$  

Type answer here

Correct Answer: 12

Deg^°

Rad

​NAMING A POLYNOMIAL

​by the number its degree

​DEGREE	NAME​	​EXAMPLE
0​	CONSTANT​	12​
1​	LINEAR​	​3x - 12
2​	QUADRATIC​	​
3​	CUBIC​	​
4​	4th DEGREE POLYNOMIAL	​

​x² + 4x - 8

4x³ - 5​x² + 4x

​9x⁴ - 2x² - 6

Multiple Choice

Name the polynomial by its degree.

$$3x^2+7x-8$$  

• constant

• linear

• quadratic

• cubic

​NAMING A POLYNOMIAL

​by the number of terms it has

​Number of Terms	​Name	​Example
​1	MONOMIAL​	​4x
2​	BINOMIAL​	​7x - 8
3​	TRINOMIAL​	​2x - 7y + 12

Multiple Select

Choose all the binomial expressions.

• -5x + 12

• 2x²

• 2y² - 2y + 2

• 19 - 7y

• 3x³ - 3

Multiple Select

Choose all the descriptions that describe the polynomial.

-4x² - 7

• trinomial

• linear

• quadratic

• binomial

• monomial

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