Polynomials Revisit

Polynomials Revisit

By Carrie Johnson

The monomial is...

a single term or product of terms

Some monomial examples are:

​

3x² 7x 4xy 3x²y⁷​

Some text here about the topic of discussion

The binomial is...

a sum of 2 monomials

Some binomial examples are:

​

3x² + 7x or x-2 or x² - 9​

Some text here about the topic of discussion

The trinomial is...

a sum of 3 monomials

Some binomial examples are:

​

x² + 5x + 6 or 3x² -6x - 9​

Some text here about the topic of discussion

The degree of a polynomial...

is the highest exponent of a polynomial​

An example of a degree 3 polyomial would by

x³ - 4x²​ + 7x - 9

Some text here about the topic of discussion

Look for the HGHEST power

​Classifying a polynomial by DEGREE

​

Multiple Choice

Name the polynomial by DEGREE:

$$9x+2$$  

• Constant

• Linear

• Quadratic

• Cubic

Multiple Choice

Classify the polynomial by degree f(𝒙) = 3x⁴ + 5x³ - x².

• quadratic

• cubic

• quartic

• quintic

Multiple Choice

Name the polynomial by DEGREE:

$$-2x^2$$  

• Constant

• Linear

• Quadratic

• Cubic

Multiple Choice

Name the polynomial by DEGREE:

$$x^4-x^3+2x+5$$  

• Linear

• Quadratic

• Cubic

• Quartic

Count how many items are separated by + and – signs

​Classifying a polynomial by TERMS​

Multiple Choice

How many TERMS does the polynomial have?

$$-27a^3+9a^2-45a$$  

• 5 terms

• 0 terms

• 2 terms

• 3 terms

Multiple Choice

A polynomial that has two terms is a:

 

• monomial

• binomial

• trinomial

• polynomial

Multiple Choice

Classify the polynomial:

$$2x^3-18x$$  

• Quadratic Binomial

• Linear Binomial

• Cubic Binomial

• Quadratic Trinomial

Multiple Choice

Classify the polynomial:

$$x^2+10x-24$$  

• Quadratic Binomial

• Linear Binomial

• Cubic Binomial

• Quadratic Trinomial

Multiple Choice

The degree of a cubic polynomial is...

• 4

• 3

• 2

• all of the above

Multiple Choice

The leading coefficient in the polynomial P(x) = 5x³ + 13x² + x + 4 is...

• 3

• 5

• 13

• 4

Multiple Choice

Multiply these Polynomial expressions. Use an area model and combine like terms.

(x + 1) (x²+ 3x + 2)

• x³ + 4x² + 5x + 2

• x³ + x² + 3x + 3

• 2x³ + 4x² + 6x + 3

• (x+1)³ (x+3)

Multiple Choice

Given P(x) = x³ + 4x² + 5x + 2 , then P(2) = ?

• 34

• (x - 2)

• 36

• 2x

Multiple Choice

Given the factorized polynomial of (x + 2)(x + 1)(x - 3), the x-intercepts are...

• {2, 1, 3}

• {2, 1, -3}

• {-3, 1, 2}

• {3, -1, -2}

Multiple Choice

(x³+ x² + x + 3) + (2x³ + 3x² + 2x + 1)

• 2x⁶+3x⁴+ 2x + 4

• 10x³ + 4

• 3x³ + 4x² + 2x + 4

• 3x³ + 4x² + 3x + 4

Multiple Select

The curve of P(x) = (x+2)²(x-3) will.........(two correct answers!!)

• Cut through the

  x-axis at (2,0) and (-3,0)

• Intercept the

  x-axis at (-2,0) and (3,0)

• Bounce on the

  x-axis at (3,0) and cut through at (-2,0)

• Bounce on the

  x-axis at (-2,0) and then cut through at (3,0)

Multiple Choice

If a Polynomial is divided by a factor such as (x + 2) and there is no remainder...

• (-2) is a factor of the polynomial

• (-2,0) is one of the x-intercepts

• P(2)=0

• All of the above

Multiple Choice

If a Polynomial is divided by a factor such as (x - 3) and there is no remainder...

• (x - 3) is a factor of the polynomial

• (3,0) is one of the x-intercepts

• P(3)=0

• All of the above

Multiple Choice

The factorized expression for the graph to the left is...

• (x-1)(x-2)(x+2)

• (x+1)(x+2)(x-2)

• (x-4)(x-1)(x+2)

• (x-1)(x-2)(x+4)

Multiple Choice

P(x) = (x - 1)(2x - 2)(x - 2) is the polynomial of the graph

• True

• False

Multiple Select

If P(3) = 0 , then which of the following is a factor?

• (x + 3)

• (3 - x)

• (x - 3)

• (x + 0)