Remainder and Factor Theorems

(2x³ + 5x² + 9) ÷ (x + 3)

• 2x² - x + 3
• 2x³ - x² + 3x
• 2x² + 11x + 33 + 108/x+3
• 2x² - 5x + 12

Tags

CCSS.HSA.APR.D.6

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9
• 3x² - 3x + 8 - 9/x+1
• 3x² + 3x + 8 + 7/x+1
• 3x³ + 3x² + 8x + 7

Tags

CCSS.HSA.APR.D.6

(2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13
• 2x³ + 4x² +3x - 1
• 2x² - 4x + 3 - 13/x-2
• 2x² + 4x + 3 - 1/x-2

Tags

CCSS.HSA.APR.D.6

(x³-3x²-10x+24) ÷ (x+3)

• x²-7x+5

• x-8

• x²-6x+8

• x+9

Tags

CCSS.HSA.APR.D.6

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13
• 2x³ + 4x² +3x - 1
• 2x² - 4x + 3 - 13/x-2
• 2x² + 4x + 3 - 1/x-2

Tags

CCSS.HSA.APR.D.6

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13
• 2x³ + 4x² +3x - 1
• 2x² - 4x + 3 - 13/x-2
• 2x² + 4x + 3 - 1/x-2

Tags

CCSS.HSA.APR.D.6

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.

Tags

CCSS.HSA.APR.D.6

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

• yes

• no

Tags

CCSS.HSA.APR.B.2

            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. 

Tags

CCSS.HSA.APR.B.2

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656
• p(2) = 652
• p(2) = -64
• p(2) = -368

Tags

CCSS.HSA.APR.B.2