Remainder Theorem for Polynomials

How could you determine    if x-2 is a factor of 2x³-5x²+x-2?

• Use synthetic division and see if the quotient is even

• Ask the person sitting next to me

• Use synthetic division and see if the remainder is zero

• Flip a coin

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. 

Find the zeros of the polynomial given one factor.

• X= 3,4,5

• x=-3,-4,-5

• x=-3,4,5

• x= 3, -4, -5

Which of these is a possible root of the polynomials?
x³ - 6x² - x + 30

• 0

• 4

• -9

• -15

When a polynomial function f(x) is divided by
 (x - 8), the remainder is 12. 
What is f(8)?

• -8

• 8

• 12

• cannot be determined

If dividing polynomial g(x) by (x – 1) yields a remainder of 2, which must be true?

• g(1) = 2

• g(-1) = 2

• g(2) = 1

• g(2) = -1

What is the remainder when 5x³-14x²-8x+5 is divided by x-3

• -13

• 10

• 13

• -10

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

• 0

• -3

• 9

• 5

You divide the polynomial g(x) by
(x - 3) and obtain a remainder of 9, what is g(3)?

• -3

• 3

• 9

• cannot be determined

What is the remainder if

(x³ - 5x² + 2x - 10) is divided by (x - 5)?

• 0

• 4

• 7

• -1