Factor and Remainder Theorems

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

• YES
• NO

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

• Yes
• No

(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

Is (x-7) a factor of (x²-5x+14)?

• Yes
• No

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

• -2
• -6
• -12
• 0

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)

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

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3
• -1,-3,3/2
• 3,3,3
• -3,2/3,-1

Match the following appropriately.

It is important you can recognize the connection between factors and solutions.

• x - 3 is a factor of p(x).

• 1 is a solution of p(x).

• x is a factor of p(x).

• 3 is a solution of p(x).

• 2x - 3 is a factor of p(x).

• 0 is a solution of p(x).

• x-1 is a factor of p(x).

• 3/2 is a solution of p(x).

Match the following appropriately.

It is important you can recognize the connection between factors and solutions.

• 5 is a solution of p(x).

• x + 5 is a factor of p(x).

• -5 is a solution of p(x).

• x + 3 is a factor of p(x).

• 5/3 is a solution of p(x).

• x - 5 is a factor of p(x).

• -3 is a solution of p(x).

• 3x - 5 is a factor of p(x).