Unit B Review Polynomials

Unit B Review Polynomials

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Here are some main success criteria

• I can describe how the degree and leading coefficient affect the graph

• I can describe the end behavior (using infinities)

• I can change factored form into standard form (box method)

• I can plug in numbers to determine if there is an x- or y-intercept at a specific point

Poll

How ready do you feel for this individual Comp tomorrow?

• Super ready

• It'll be okay

• I'm nervous

• I'm NOT ready

Even vs Odd Degree

• Degree means the highest exponent (in standard form)

• Even could be 2, 4, 6, 8....

• Even degree makes a graph have both ends going the same way

• Odd could be 1, 3, 5, 7...

• Odd degree makes one end go up and the other down

Multiple Select

Which are even Degree?

Multiple Select

Which are even Degree?

Multiple Select

Which are ODD Degree?

Leading Coeffcients

Leading Coefficient is the Number multiplied with the x of highest exponent

Multiple Choice

What's the leading coefficient of

 $3x^2+5x^3-2x^{10}$  

• 5

• 10

• 2

• -2

• 3

Leading Coefficients

• POSITIVE Leading Coefficients make EVEN degree polynomials open up

• Negative LC make EVEN degree polynomials open down

• Positive LC make ODD degree polynomials "increasing"

• Negative LC make ODD degree polynomials "decreasing"

Multiple Select

Which are Even Degree AND Positive Leading coefficient?

Multiple Select

Which are ODD Degree and NEGATIVE leading coefficient?

Multiple Choice

Which would best describe this equation?

 $3x^9-7x^2+x+2$  

• Odd degree, Negative leading coefficient

• Even degree, Negative leading coefficient

• Odd degree, Positive leading coefficient

Multiple Select

Which would best fit this equation?

 $3x^9-7x^2+x+2$  

Multiple Choice

Which best describes this equation?

 $3x-7x^2+x^8+2$  

• Even degree, Positive LC

• Even degree, Negative LC

• Odd degree, Negative LC

Multiple Select

Which would best fit this equation?

 $3x-7x^2+x^8+2$  

Multiple Choice

 $3x^6+7x^6$  = ?

•  $10x^{12}$  

•  $10x^6$  

Multiple Choice

 $3x^6\cdot7x^6$  = ?

•  $21x^{12}$  

•  $10x^6$  

What about factored form?

• We have to multiply things out to find the degree and leading coefficient

• Factored form has multiplication between parentheses

Multiple Choice

Which is factored form?

• $x^{5\ }-2x\ +\ 1\ \left(x-3\right)$

• $4x\left(3x-2\right)\left(x^4-5\right)$

• $100x^{99}+x-9$

Poll

Predict the degree of this polynomial (after we put it in standard form using the box method)

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

• 2

• 4

• 3

• 5

Multiple Choice

What is the degree of this polynomial (after we put it in standard form using the box method)

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

• 2

• 4

• 3

• 5

Multiple Choice

What is the LEADING COEFFICIENT of this polynomial (after we put it in standard form using the box method)

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

• 2

• 4

• 3

• 5

Multiple Choice

What is the LEADING TERM of this polynomial (after we put it in standard form using the box method)

 $\left(7x-2\right)\left(x^2+1\right)\left(3x^4-5\right)$  

•  $21x^7$  
  

•  $3x^4$  
  

•  $3x^6$  

Multiple Select

Which would best fit this equation?

 $\left(7x-2\right)\left(x^2+1\right)\left(3x^4-5\right)\ =21x^{7\ }+\ ........$  

Multiple Choice

What is the LEADING TERM of this polynomial (after we put it in standard form using the box method)

 $3x\left(2x-2\right)\left(x+1\right)\left(2x^{10}-5\right)$  

•  $12x^{13}$  
  

•  $2x^{10}$  
  

•  $4x^{12}$  

Multiple Select

Which would best fit this equation?

 $3x\left(2x-2\right)\left(x+1\right)\left(2x^{10}-5\right)=12x^{13}+\ ........$  

Multiple Select

Which would best fit this equation?

 $5x\left(3x-2\right)\left(x^5+1\right)\left(x-5\right)\ =??$  

Here are some main success criteria

• I can describe how the degree and leading coefficient affect the graph

• I can describe the end behavior (using infinities)

• I can change factored form into standard form (box method)

• I can plug in numbers to determine if there is an x- or y-intercept at a specific point

Poll

How ready do you feel for this individual Comp tomorrow?

• Super ready

• It'll be okay

• I'm nervous

• I'm NOT ready