Factor and Remainder Theorem Review

If P( -4) = 0, which of the following statements is true about P(x)?

• x+4 is a factor of P(x)

• P(x) = 0, has four negative roots

• 4 is a root of P(x) = 0

• P(0) = - 4

What is the remainder when (10x⁷⁹ – 6) is divided by (x-1)?

• 4

• 3

• 2

• 1

Which polynomial when divided by (x - 2) equals (x² – x – 3) with a remainder of -3 ?

• x³ + 3x² – x + 3

• x³ – 3x² + x + 3

• x³ – x² – x + 3

• x³ – 3x² – x + 3

What is the remainder when y⁴ – 2y³ + y – 2 is divided by y - 2?

• 0

• 3

• 5

• 10

Given (2x³ – 2x² + x + 4) divided by x – 4, what is the remainder?

• 111

• 107

• 104

• 84

x – 1 is a factor of 2x³ – x² + 2x - 3

• 
• 

What is the remainder when (9x + 8x² +7x³ + … + x⁹) is divided by (x+1)?

• 8

• 6

• -5

• -9

Let f(x) = 4x^2 -33x -27. Is x - 9 a factor of the function?

• yes

• no

(x³-3x²-10x+24) ÷ (x+3)

• x²-7x+5

• x-8

• x²-6x+8

• x+9

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.