Polynomial Vocabulary with questions

Polynomial Vocabulary, Sum and Difference with questions

Coefficient, Variable, Term

A Coefficient is a number used to multiply a variable: EX 5x², 5 is the coefficient.

A Variable is a letter or symbol used to stand in for a number we don't know. EX 4a, a is the variable

A Term is a number, a variable or the product of numbers and variables. EX These are all terms: 7, x, ac³, 4pqr

Expression, Standard Form, Leading Coefficient, Constant Term

An Expression is a collection of terms that are added or subtracted. EX These are expressions: 5x, 3a + 4, 7x²-2x+9

An Expression is in Standard Form if the term with the highest degree (exponent) is first and the other terms are in decreasing order by degree.

The Leading Coefficient is the coefficient of the first term when written in Standard Form.

A Constant Term is a number without a variable.

Given the expression: 4x + 3x³ - 9 - x²

Write in Standard form: 3x³ - x² + 4x - 9

What are the coefficients? 3, -1, 4

What is the constant term? -9

What is the leading coeffiecient? 3

Adding Polynomials

If the polynomials are added, just drop the parenthesis and combine like terms.

(3x² -2x + 5) + (5x² +4x + 6) =

3x² -2x + 5 + 5x² + 4x + 6 =

8x² +2x + 11

Subtracting Polynomials

To Subtract Polynomials, you must distribute the subtraction sign, then combine like terms.

(4x² - 8) - (3x² - 12) the subtraction sign goes with each term in the ( )

4x² - 8 - (3x²) - (-12)=

4x² -8 -3x² +12 = 4x² -3x² -8 +12

x² + 4

Multiple Choice

Simplify:

(8x³ - 3x² + 9) + (5x² -6)

• 13x³ -3x² +15

• 8x³ +2x² +3

Multiple Select

Simplify:

(5x - 2x² - 6) - ( 4 + 7x - 5x²)

• -7x² + 12x -2

• 9x + 5x² + 10

• 3x² - 2x - 10

Classification by number of terms

Expressions made up of terms are called Polynomials (a polynomial will never have a variable in the denominator of a fraction)

4x³ is a Monomial because it is made up of ONE term

7a⁴ + a² is a Binomial because it is made up of TWO terms

x² + 3x -7 is a Trinomial because it is made up of THREE terms

If an expression has FOUR or MORE terms, it is just called a Polynomial

Multiple Select

4x² - 3 is a _______

• Monomial

• Binomial

• Trinomial

Multiple Select

x⁵ - 3x³ +x² + x - 1 is a ________

• Monomial

• Binomial

• Polynomial

• Trinomial

Classification by Degree - the degree of a polynomial is the value of the highest exponent

8 is Constant it is said to have a degree of 0

6x + 3 is Linear and has a degree of 1 (graphs to be a straight line)

8a² - a + 2 is Quadratic and has a degree of 2 (graphs to be a parabola)

9m³ -5m² +6m - 3 is Cubic and has a degree of 3

Multiple Select

4x² - 3x + 2 is ____________ because it has a degree of ________

• Constant, 0

• Linear, 1

• Quadratic, 2

• Cubic, 3

Multiple Select

11a³ is ____________ because it has a degree of _________

• Constant, 0

• Linear, 1

• Quadratic, 2

• Cubic, 3

Multiple Select

33 is ____________ because it has a degree of ________

• Constant, 0

• Linear, 1

• Quadratic, 2

• Cubic, 3