Synthetic Division, Remainder Theorem and Factor Theorem

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0
• 2x-10
• -2x-10
• 2x+10

Tags

CCSS.HSA.APR.B.2

Is (x-4) a factor of (x³ +x² -16x-16)?

• YES
• NO

Tags

CCSS.HSA.APR.B.2

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes
• No

Tags

CCSS.HSA.APR.B.2

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

• 2x³ - x² + x + 9
• 2x² - x + 1
• 2x² - x + 1 + 9/x-2
• 2x² - 9x - 15 - 23/x-2

Tags

CCSS.HSA.APR.D.6

Is (x-7) a factor of (x²-5x+14)?

• Yes
• No

Tags

CCSS.HSA.APR.B.2

What is the remainder when a³ - 4 is divided by a+2? 

• -2
• -6
• -12
• 0

Tags

CCSS.HSA.APR.B.2

Use synthetic division to determine f(-3), if
f(x)= (3x³ -5x² -4x +1).

• -25
• 25
• 113
• -113

Tags

CCSS.HSA.APR.D.6

Find all the factors of   x³ -3x² -4x +12 given that -2 is a zero.

• (x-2) (x+2) (x+3) 
• (x-2) (x-2) (x+3)
• (x+2) (x+2) (x+3)
• (x-2) (x+2) (x-3)

Tags

CCSS.HSA.APR.B.2

If f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

• 0
• 10
• 15
• -7

Tags

CCSS.HSA.APR.D.6

Find all the real zeros of the function 
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

• x = 1/2, -6
• x = -1/2, 6
• x = 4, -1/2, 6
• x = -4, 1/2, -6

Tags

CCSS.HSA.APR.B.2