The Remainder and Factor Theorem

P(x) = x^3 – 7x + 5 ; x-1

• factor

• not a factor

P(x) = x^3 – 7x + 5 ; x+1

• factor

• not a factor

P(x) = x^2 +4x + 4 ; x+2

• factor

• not a factor

If dividing polynomial g(x) by (x – 5) yields a remainder of 3, which must be true?

• g(5) = 3

• g(-5) = 3

• g(3) = 5

• g(3) = -5

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

When (9x⁴- 45x³ + 37x² + x +2) is divided by (x-2), find the remainder.

• 656

• 652

• -64

• -368

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. 

If (2x²+10) is divided by (x -1), then what is the remainder?

• 12

• 0

• -12

• 8

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

Decide if (x-3) is a factor of 3x³+10x²-x-12

• Yes, it is a factor!

• No, it is not a factor!