Intro to Polynomial Functions

Intro to Polynomial Functions

Multiple Choice

Which of the following expressions is in STANDARD FORM?

• $x^3+\ 5x\ -2x^2+8$

• $6x^5+3x^2-2x+1$

• $5+2x+3x^2$

STANDARD FORM

• term with the largest exponent goes first

• exponents decrease in order

Multiple Choice

Which expression is in STANDARD FORM?

• $-3x^3+x^2+5$

• $5+2x-3x^2$

• $4x^4+3x-2x^2-8$

Multiple Choice

What is the DEGREE of the expression

 $4x^3+2x^5-8x+1$  

• 3

• 5

• 1

• 0

Multiple Choice

What is the degree of

 $12x-5x^2+x^3$  

• 1

• 2

• 3

• 12

Multiple Choice

What is the degree of

 $2x^6-12x^5+x^2-3x$  

• 1

• 2

• 5

• 6

The DEGREE of a Polynomial is the HIGHEST EXPONENT

• must be written out in standard form

• no parenthesis

• the LEADING COEFFICIENT will always be in front of the variable with the highest exponent

Multiple Choice

What is the degree of

 $4-3x^7-12x^2+5x$  

• 7

• 2

• 1

• 12

Multiple Choice

What is the degree of

 $2x^3\left(x+1\right)\left(x^2-2\right)$  

• 6

• 5

• 3

• 2

Remember there are no ( ) in standard form

Just add all the exponents

Don't forget x is the same as x¹

~~ the one is included in adding the exponents

~~ the coefficients do not affect the degree

Multiple Choice

What is the degree of

 $123x\left(76x^3+1\right)\left(99x^5-2\right)$  

• 3

• 5

• 8

• 9

Multiple Choice

What is the LEADING COEFFICIENT OF

 $3x^4+8x^2-10x+1$  

• 3

• 8

• -10

• 1

Multiple Choice

What is the leading coefficient of

 $4+8x-2x^3$  

• 4

• 8

• -2

• 3

Multiple Choice

What is the leading coefficient of

 $x^4+25x^3-8x+9$  

• 1

• 25

• 0

• -8

• 9

Multiple Choice

This is the graph of

 $y=x^{2\ }+8x\ -5$  What's the degree and how many roots?

• 2; 2

• 8; 2

• -5; 2

Multiple Choice

This is the graph of

 $y=x^3-4x+1$  What's the degree and how many roots?

• 3; 3

• -4; 3

• 1; 3

Multiple Choice

This is the graph of y=2x⁴+3x³-x²-x What is the degree and how many roots?

• 4; 4

• 3; 4

• 1; 4

Catching on to the Pattern???

• The degree tells you how many ROOTS

• Fundamental Theorem of Algebra

• memorize this!!!!!!

You might have noticed one more thing...

• Let's go back and check out the number of turns

• How do they relate to the degree??

Multiple Choice

2nd degree Polynomial has ____ turns

• 0

• 1

• 2

• 3

Multiple Choice

3rd degree polynomial has ____ turns

• 0

• 1

• 2

• 3

Multiple Choice

4th degree polynomial has ____ turns

• 0

• 1

• 2

• 3

• 4

Multiple Choice

An 8th degree polynomial with have ___ roots and ____ turns

• 8; 7

• 8; 8

• 7; 8

• 9;8

ALMOST THERE....

• Let's take a look at END BEHAVIOR

• The degree and the leading coefficient will play a big role

This shows EVEN degree functions with a leading coefficient of +2 What do you notice about the ends?

This shows EVEN degree functions with a leading coefficient of -2 What do you notice about the ends?

This shows ODD degree functions with a leading coefficient of +2 What do you notice about the ends?

This shows ODD degree functions with a leading coefficient of -2 What do you notice about the ends?

Multiple Choice

Give it a try... What's the degree and the leading coefficient?

• degree is odd; LC is +

• degree is odd; LC is -

• degree is even; LC is +

• degree is even; LC is +

Multiple Choice

Give it another try... What is the degree and LC?

• degree is odd; LC is +

• degree is odd; LC is -

• degree is even; LC is +

• degree is even; LC is -

And that is our Intro to Polynomial Functions

Get ready to sum all this up in your notes and demo your understanding!