Polynomials Review

Polynomials

Vocabulary, Classifications, and Operations

Polynomials Vocabulary

● Variable (a letter) - represents a quantity that can

vary or change

● Constant (not changing fixed) - a number or symbol

for a non-changing value (6, 234, 𝜋 ) that is NOT
next to a letter (not being multiplied by a variable)

● Coefficient - a number or value NEXT TO A

LETTER or variable that acts as a multiplier
(including the invisible 1)

Polynomials Vocabulary

● Monomial - a number, a variable, or the product

of a number and one or more variables (1 term)

● Binomial - polynomial with 2 terms
● Trinomial - polynomial with 3 terms
● Polynomial - a monomial or the sum of

monomials (4 terms or more)

In your notebook, write the expression below and label it
(like in the examples above) with these vocabulary words:
Constant, Variable, Coefficient, Exponent, Base, Term.

Multiple Choice

Classify the following polynomial

• quartic polynomial

• quadratic polynomial

• quartic trinomial

• quadratic trinomial

Multiple Choice

Classify the following polynomial

• quadratic trinomial
• cubic binomial

Multiple Choice

Classify the polynomial:
3x² – 8x + 1

• quadratic trinomial

• cubic trinomial

• quadratic binomial

• cubic binomial 

Multiple Choice

Is this expression in Standard Form?
6w² - 9w³

• Yes

• No

Multiple Choice

What is the degree?
 - 3x³ - x² - 10x + 12

• 1

• 2

• 3

• 4

​POLYNOMIAL

​poly- "many" -nomial "term"

Term(s) whose exponents are whole numbers, and are separated by a "+" or a "-"

​EXAMPLES

​x + 4

​x² + 8x - 4

​z⁵ - z⁴ + x³ + 2x - 10

​EXAMPLES

​How many terms does each polynomial have?

​x + 4

​x² + 8x - 4

​z⁵ - z⁴ + 2x - 10

​TERM

- a number  (ex: 5)

- a variable (ex: y)

- the product of a number and variable (ex: 3x)

- the product of a number and variables (ex: 8xy)

​EXAMPLE

2​ab + 4

1^st term

2^nd term

​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

​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

Multiple Choice

Simplify:

$$5\left(3x+2\right)$$  

• $$3x+10$$

• $$15x+10$$  

• $$15x-10$$  

• $$3x-10$$  

Multiple Choice

(x + 5)(x + 4)

• x² + x + 20

• x² + 20x + 9

• x² + 9x + 20

• x² - 9x + 54