Synthetic Division and Factor Theorem

• x - 7
• x² - 7
• x + 7
• x² + 3x - 54

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

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

What does it mean to be a factor of a number?

• Divides evenly with a remainder of zero.
• Divides unevenly with a remainder of 1.

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

What should be the order of the polynomial coefficients if

(3x - 4x³+ 6x⁴ + 1)

• 3 0 -4 6 1

• 6 -4 3 1 0

• 6 -4 0 3 1

• -6 4 0 -3 -1

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

Is this division problem worked correctly?

• This is correct!
• This is incorrect!

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

• 0
• 1
• 2
• 3