Synthetic Division, Remainder Theorem and Factor Theorem

Based on the remainder you found, which statement is true?

Assume that a polynomial has a solution at the x-value 4. Which of the following must be a factor of that same polynomial?

• 4x

• x-4

• x+4

Assume that x-2 is a factor of a polynomial. Which x-value must be a solution of that same polynomial?

• The x-value -2

• The x-value 2

• The x-value 0

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

• -5 is a solution of p(x).

• x + 3 is a factor of p(x).

• 5/3 is a solution of p(x).

• 3x - 5 is a factor of p(x).

• 5 is a solution of p(x).

• x + 5 is a factor of p(x).

• -3 is a solution of p(x).

• x - 5 is a factor of p(x).

• True

• False

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25

• 25

• 113

• -113

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

• x + 1

• x + 2

• x + 5

• x + 10

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

• -2

• -6

• -12

• 0

Which binomial is a factor of
f(x)= x³ + x² -24x +36?

• x + 2

• x + 3

• x + 6

• x + 9

Which binomial is a factor of
f(x)= 6x³ -35x² +34x +40?

• 2x - 3

• 2x - 5

• 3x - 2

• 5x - 2