Dividing Polynomials with Remainders

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

• 4
• 7
• 2
• 11

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

For synthetic division, what would be the number in the left hand box?

• 0
• 1
• 2
• 3

            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. 

Divide using synthetic division 
(2x³ + 4x² - 5) by (x + 3).

• 2x² + 2x - 4  R(-12)
• 2x² - 2x + 6  R(-23)
• 2x² - 2x + 8  R(-20)
• 2x² - 4x + 1  R0

2x³ - 5x² + 3x + 7 ÷ x - 2

• 2x³ - x² + x + 9
• 2x² - x + 1
• 2x² - x + 1 + 9/x-2
• 2x² - 9x - 15 - 23/x-2

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

Find the Quotient
(2x³ - 5x² - 3x + 7) / (x - 2)

• 2x²- 9x +15
• 2x² - x - 5
• 2x² - 9x - 21
• 2x² + x + 5

Classify by degree of polynomial:
3x³ – 6x

• Constant
• Linear
• Quadratic
• Cubic

Factor completely:
x³ + 3x² - 4x - 12

• (x + 3)(x² - 4)
• (x + 3) (x + 2)(x - 2)
• (x² + 4) (x - 3)
• (x² + 3)(x - 4)