3-6 (Theorem of Alg.) / 3-7 (Graphs of Polynomials)

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

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

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

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

List the potential real zeros of:
f(x) = 5x³ - x² + 3

• ±1/5, ±3/5, ±1, ±3
• ±1/3, ±5/3, ±1, ±5
• ±1/5, ±3/5, ±1, ±3, ±5
• ±1/5, ±1/3, ±1, ±3, ±5

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x) = (x+2)(x-1)(x-4)

• f(x) =x³ - 3x² - 6x + 8

• f(x) = x³ + 8

• f(x) = x³ - 3x² + 8

Tags

CCSS.HSA.APR.B.3

Find all zeros.

y = x⁴ - 3x³ + 4x² - 8

• 1, -2, (2±2i√3)/2

• -1, 2, (2±2i√3)/2

• 1, -2, (2±2i√5)/2

• -1, 2, (2±2i√5)/2

Find all zeroes given a factor of (x+3).

y = 2x³ + 5x² - 6x - 9

• -1,-3,-3

• -1,-3,3/2

• 3,3,3

• -3,2/3,-1

Tags

CCSS.HSF-IF.C.7C

Write the simplest polynomial in standard form with roots -5/2,  $\sqrt{7}$  , and 0.

•  $f\left(x\right)=2x^3+5x^2-14x-35$  

•  $f\left(x\right)=2x^4+5x^3-14x^2-35x$  

•  $f\left(x\right)=2x^3+5x^2-13x-35$  

•  $f\left(x\right)=2x^4+12x^3-14x^2-35x$  

Tags

CCSS.HSA.APR.B.3

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 4, 2, or 0

• 4

• 3 or 1

• 3

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11