Unit 4 Review: Polynomial Operations

Factor completely: 
x⁴-10x²+9

• (x-9)(x-1)
• (x²-9)(x²-1)
• (x-3)(x+3)(x²-1)
• (x+3)(x-3)(x+1)(x-1)

x⁴ - 4x² - 45

• (x² - 5)(x - 3)(x + 3)
• (x² + 45)(x + 1)(x - 1)
• (x² + 5)(x - 3)(x + 3)
• (x² + 3)(x - 5)(x + 3)

x⁴ - 48x² - 49

• (x² - 7)(x - 7)(x + 1)
• (x² + 49)(x² + 1)
• (x - 7)(x - 7)(x² + 1)
• (x + 7)(x - 7)(x² + 1)

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function?

• yes
• no

Let f(x) = 4x² -33x -27.  Is k = 9 a zero of the function?

• yes
• no

(2x³ + 5x² + 9) ÷ (x + 3)

• 2x² - x + 3
• 2x³ - x² + 3x
• 2x² + 11x + 33 + 108/x+3
• 2x² - 5x + 12

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9
• 3x² - 3x + 8 - 9/x+1
• 3x² + 3x + 8 + 7/x+1
• 3x³ + 3x² + 8x + 7

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

• 0
• 10
• 15
• -7

            Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.
• No, (x-2) is  not a factor. The remainder is zero.
• Yes, (x-2) is a factor. The remainder is zero.
• No, (x-2) is  not a factor. There is a remainder. 

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

• 3   0   -4   6   1
• 6   -4   3   1   0
• 6   -4   0   3   1
• -6   4   0   -3   -1