Polynomials May 2021

Polynomials May 2021

A term

A polynomial is made of terms that are added together or just one term.

A number with no variable is a constant term.

If a term has a number it is an algebraic or variable term.

Each algebraic term has a coefficient and an exponent.

An algebraic term

The coefficient is the factor in front of the variable. If the factor is one then we usually do not write it.

 $4n^3$  coefficient is 4, exponent is 3

 $n^8$  coefficient is 1, exponent is 8

 $7n$  coefficient is 7, exponent is 1

Terms are classified by degrees

A term with a variable raised to an exponent of 3 is called a cubic term. It is degree 3.

A term with a variable raised to an exponent of 2 is called a quadratic term. It is Degree 2

A term with a variable raised to an exponent of 1 or no exponent is called a linear term. It is Degree 1

No variable is a constant term. It is Degree 0

Polynmials do not have negative degrees.

Degree of the polynomial

The polynomial is described by the highest degree in the polynomial.
 $4y^3$  is a cubic polynomial and degree 3

 $7y$  is a linear polynomial and degree 1
 $12y^2-4y+7$  is a quadratic polynomial  and degree 2
 $y^6+7$  is degree 6

Classifying Polynomials by terms

Polynomials can have one term or more.

If it has just one term it is called a monomial.

If it has two terms it is called a binomial.

If it has three terms it is called a trinomial.

And if it has more than three terms it is just called a polynomial.

Multiple Choice

 $3x^2+3$  is a

• binomial

• trinomial

• monomial

• polygon

Multiple Choice

 $5x^2+3x-4$  is a

• binomial

• trinomial

• monomial

• polygon

Multiple Choice

 $5h^4+3h-4h^2+7$  is a

• binomial

• trinomial

• monomial

• polygon

Multiple Choice

 $3r$  is a

• binomial

• trinomial

• monomial

• polygon

Standard Form

A polynomial is in standard form when the highest exponents are first. All like terms must be combined.  The exponents should decrease from left to right. The constant term is considered to have an exponent of zero.

 $5t^4+6t^2-4t+6$  is in standard form

 $8-4x^2+6x^3-7x$  is not

All monomials are in standard form

Multiple Choice

Which polynomial is in standard form?

• $d^4-d^7$

• $4-d$

• $d^3-9$

• $d^2+7d^4-9$

Multiple Select

Select all polynomials that are in standard form

• $m^3+4m-12$

• $m+7$

• $43$

• $8-m^3$

• $m^2+8m-5$

Multiple Choice

 $5t^5+7t^4\$  ____  $t^2-7$  
which term would go in the blank to make it in standard form?

•  $5t^4$  

•  $-t^3$  

•  $6t^2$  

• 5

Leading Coefficient

When a polynomial is in standard form, the coefficient of the first term is called the Leading Coefficient. It should be the coefficient of the term with the highest degree.

Multiple Choice

Which is an example of a quadratic monomial?

• x³ + 5

• x² + 3

• x² + 5x - 6

• -5x²

Multiple Choice

Classify the polynomial by its number of terms 4x² - 2

• monomial

• binomial

• trinomial

• polynomial

Multiple Choice

What is the constant of this polynomial? 2x³ - 8x² + 3x - 7

• 2

• -8

• 3

• -7

Multiple Choice

What is the leading coefficient of the following polynomial?

5x² - 3x + 6

• 2

• -3

• 5

• 6

Multiple Choice

Which is an example of a cubic binomial?

• x³ + 5

• x² + 3

• x² + 5x - 6

• 5x³

Multiple Choice

Which is an example of a linear polynomial?

• x² - 5

• 6x + 4

• 5x⁵

• 2x³ - 9x²

Multiple Choice

What is the term classification of the following polynomial?

x³ - 7x² +3

• monomial

• binomial

• trinomial

• polynomial

Multiple Choice

What is the degree classification of this polynomial?

x² + 4x -8

• binomial

• trinomial

• quadratic

• cubic

Multiple Choice

Terms in a polynomial are separated by what?

• Parenthesis

• Multiplication/

  Division

• Constants

• Addition/

  Subtractraction

Multiple Choice

Which is an example of a cubic monomial?

• x³ + 5

• x² + 3

• x² + 5x - 6

• 5x³

Multiple Choice

Use the FOIL method to multiply:
(x+10)(x-10)

• x²  - 100
• x² + 100
• x² + 20x - 100
• x² -20x + 100

Multiple Choice

Use the FOIL method to multiply:
(x +2)(x + 3)

• x² + 5x + 6
• x² + x + 6
• x² + 5x + 5
• x² + 6x + 6

Multiple Choice

Find the product:
-3x²(5x² + 3x)

• -15x⁴ - 9x²
• -15x⁴ - 9x³
• 15x⁴ - 6x³
• -15x⁴ + 9x³

Multiple Choice

Subtract the following polynomials:
(7p + 4p³ - 8) - (-3p² + 2 - 9p)

• -3p² + 4p³ -15 + 9
• 3p³ + 4p² - p + 3
• 4p³ +3p² +16p -10
• 4p³ +3p² + 16p + 10

Multiple Choice

Add the following polynomials:
 (5x + 2) + (4x + 5)

• 9x -7
• -9x-11
• 9x+7
• x+7

Multiple Choice

Add the following polynomials:
 (5x + 2) + (4x + 5)

• 9x -7
• -9x-11
• 9x+7
• x+7

Multiple Choice

Add the following polynomials: 
(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

• 11x⁴  + 2x² + 14x
• 16x⁴  + x² + 14x
• 11x⁴  + x² + 14x
• 11x⁴  + 2x² + 10x

Multiple Choice

Combine like terms:
5x²+ x - x²+ 4x

• 6x² + 5x
• 4x² + 3x
• 4x² + 5x
• 5x² + 5x

Multiple Choice

Combine Like Terms:
2x - 4x + 12x²

• 12x² - 2x
• 10x
• 10x²
• 12x² + 2x

Multiple Choice

Combine Like Terms:
4y + 3x³ + 2y + 8x³ - 6y

• 11x³
• 11x³ + 12y
• 5x³
• 11x⁶

Multiple Choice

Which polynomial is written in standard form?

• 8x - 11x²
• 4x³ + 7x - 9
• 12 + 4x
• 13x + 7x² - 9x³ + 12

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11
• 9x³ + 8x² - 3x - 11
• 8x² + 9x³ -11 - 3x
• -11 - 3x + 8x² + 9x³

Multiple Choice

Combine like terms
3x + 2x + 3y - 7y

• 5x + 10y
• 5x + 4y
• 5x - 4y
• 5x -10y

Multiple Choice

Simplify this polynomial:

n - 10 + 9n - 3

• -3

• 9n - 3

• n

• 10n - 13

Multiple Choice

Simplify this polynomial:

3x² - x + 2 - 5x² + 8x - 5

• 8x² + 9x + 7

• -2x² + 7x - 3

• 2x² + 7x - 3

• 5x² - 3

Multiple Choice

Which pair is an example of like terms?

• 2a and 2b
• x and x²
• 3k and 3k³
• y² and 2y²

Multiple Choice

The number in front of the variable is called the.... 

• exponent
• base
• coefficient
• fronter

Multiple Choice

What are like terms?

Terms that have....

• the same variables

• the same exponents

• the same coefficients

• the same variables and exponents

Multiple Choice

Classify:
2n³

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

What is the the DEGREE:

4x³ - 5x² + 2x - 1

• 1

• 2

• 3

• 4

Multiple Choice

Simplify the Expression:

3x + 6 - 2x +7

• 14

• 14x

• x + 13

• x - 13

Multiple Choice

Classify by number of terms:

5x² – 6x + 3

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

What is the coefficient of this term?

9x³

• None

• 9

• 3

• x

Multiple Choice

What is the constant of this polynomial?

2x³ - 8x² + 3x - 7

• 2

• -8

• 3

• -7

Multiple Choice

What is the degree of this polynomial?

2x⁴ - 3x⁵ + x

• -3

• 2

• 4

• 5

Multiple Choice

How many terms are in this polynomial?

2x³ - 8x² + 3x - 7

• 7

• 1

• 4

• 2

Multiple Choice

Classify by number of terms:

3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial