Polynomial Review Part 2

Factor by GCF:
56a³ - 8a

• 8a²(56a³-8a)
• 8a(7a²-1)
• 8a(7a³-a)
• 8a²(35a²-a)

Factor:
 2n²-8n³

• 2n²(n-4n²)
• 2n²(1-4n²)
• 2n³(10-8n²)
• 3n(1-4n)

x² - 25

• ( x + 5 ) ( x - 5 ) 
• ( x - 5 ) ( x - 5 ) 
• ( x + 5 ) ( x + 5 ) 
• Prime

The degree of a polynomial can be determined by the largest powered monomial of the polynomial.  
What is the degree of the polynomial:
f(x) = 3x² + 4x - 5

• Degree 2  (quadratic)
• Degree 3 (cubic)
• Degree 4 (quartic)
• Degree 5 (quintic)

The degree of a polynomial can be determined by the largest powered monomial of the polynomial.  
What is the degree of the polynomial:
f(x) = -4x³ + 5x - 2

• Degree 2 (quadratic)
• Degree 3 (cubic)
• Degree 4 (quartic)
• Degree 5 (quintic)

The leading coefficient is the coefficient of the largest degree monomial for the polynomial.
What is the leading coefficient for the polynomial f(x) = 2x³ + 4x - 5

• The leading coefficient is 2
• The leading coefficient is 3
• The leading coefficient is 4
• The leading coefficient is 5

The leading coefficient is the coefficient of the largest degree monomial for the polynomial.
What is the leading coefficient for the polynomial f(x) = -4x³ - 2x + 5

• The leading coefficient is -2
• The leading coefficient is 3
• The leading coefficient is -4
• The leading coefficient is 5

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.  
Enter the polynomial function into a graphing calculator or online graphing tool to determine the end behavior.
f(x) = 2x³ - x + 5

• Left up    Right up
• Left up   Right down
• Left down   Right up
• Left down   Right down

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Describe the end behavior of the graph.

• x → ∞, y→ ∞ and
  x→ ∞, y→⁻∞
• x → ∞, y→ ∞ and
  x→⁻∞, y→∞
• None of these
• x →∞,y→⁻∞ and
  x→∞, y→⁻∞

Tags

CCSS.HSF-IF.C.7A