Factors of Polynomials and Synthetic Divisions

• 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

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

The answer to a division problem is known as the...?

• product
• sum
• difference
• quotient

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

If 𝒙²+𝟑𝒙+𝟕 is divided by  𝒙+𝟐, then what is the remainder?

• 0
• -3
• 9
• 5

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3
• -1,-3,3/2
• 3,3,3
• -3,2/3,-1