Solving Polynomial Equations by Factoring, Real and Imaginary

Factor completely given (x-4) is a factor. 
x³ - 4x² -4x + 16

• (x+4)(x+2)
• (x-4)(x -2)(x + 2) 
• (x+4)(x² -4)
• (x-4)(x-2)

Tags

CCSS.HSA.APR.B.2

Decide if (x-3) is a factor of 3x³+10x²-x-12

• Yes, it is a factor
• No, it is not a factor

Tags

CCSS.HSA.APR.B.2

How many roots does the polynomial have? 
And what are the possible combinations of real and imaginary roots? 
y = 3x⁴ - 8x² + 7x - 1

• 7 roots. 
  Possibly 7, 5, 3 or 1 real with 7, 5, 3 or 1 imaginary.
• 7 roots. 
  Possibly 7, 5, 3 or 1 real with 0, 2, 4 or 6 imaginary. 
• 4 roots. 
  Possibly 4 or 2 real with 0 or 2 imaginary.
• 4 roots.
  Possibly 4, 2 or 0 real with 0, 2 or 4 imaginary

Tags

CCSS.HSN.CN.C.9

If a polynomial has zeros at 0, 3, and -5/4, what are the factors? 

• x, (x + 3), and (4x - 5)
• x, (x - 3), and (4x + 5) 
• x, (x - 3), (x + 5),
  and (x - 4)
• (x - 3) and (x + 5/4)

Tags

CCSS.HSF-IF.C.7C

Graph the polynomial on your grapher. 
Over which interval is it increasing? 

• (-5.69, infinity)
• [1.48, infinity]
• (1.48, infinity)
• [-5.69, infinity]

Factor completely 2x² - 9x - 35

• (2x - 7)(x + 5)
• 2(x - 7)(x + 5)
• (2x + 5)(2x - 14)
• (2x + 5)(x - 7)

One root of 2x³-13x²+36 is 2.
What is another zero?

• 3/2
• 6
• 2
• -6

How many roots does ...  2x³ + 8x² + 3x + 9 = 0 have based on the Fundamental Theorem of Algebra?

•  3 or less roots
• 6 or less roots
• exactly 3 roots
• 3 or 1 roots

Tags

CCSS.HSN.CN.C.9

What are the roots of the following factored polynomial?
(x+1)(x-1)(2x+1)=0

• x= -1/2, -1, 1
• x= 1/2, -1, 1
• x = - ± 1
• x= 1/2, 1

Tags

CCSS.HSF-IF.C.7C

Which binomial is not a factor of ....... x³ +4x²+x - 6

• (x-1)
• (x+2)
• (x-4)
• (x+3)

Tags

CCSS.HSA.APR.B.2