Division of Polynomials with No Remainder

How can I tell, when doing synthetic division, if the binomial is a FACTOR of the dividend?

• The remainder is zero

• They are all factors

• We can't tell

• The remainder is a constant

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. 

x - 7 x² - 7 x + 7 x² + 3x - 54

• x - 7

• x² - 7

• x + 7

• x² + 3x - 54

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)

• x + 5 + (2/2x - 4)
• x - 8
• x - 5 + (3/2x - 4)
• x + 5

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

• True

• False

• Only for the dividend

• Only for the divisor

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0

• 2

• 4

• 6

What is the quotient when (10n² - 37n - 12) is divided by (n - 4)?

• (10n - 3)

• (3n - 10)

• (10n + 3)

• (3n + 10)

• 2x³ + 3x + (7/x-4)
• 2x² + 3x + 8 + (7/x-4)
• 2x² + 3x + 8
• 2x² - x + 10 + (6/x-4)