Long Division and Remainder Theorem

What is the remainder when

 $x^3+x^2-2x+3$  is divided by  $x-1$  ?

• 3

• 5

• 7

• 1

What is the remainder when  $2x^3+x^2-3x+2$  is divided by  $x-2$  ?

• 16

• 4

• 8

• 2

What is the remainder when  $x^3-x^2+2x-5$  is divided by  $x-2$  ?

• 3

• 21

• -3

• 9

  $\left(x+1\right)$  is a factor of $f(x)=x^3-6x^2+3x+10$ .

• TRUE

• FALSE

Which is a linear factor of $f(x)=x^3+x^2-24x+36$  ?

• x + 2

• x + 3

• x + 6

• x + 9

What is the remainder of  $(3x^3-5x^2-4x+1)\ ÷\ (x+3)$  ?

• -25

• 25

• 113

• -113

  $\left(x+5\right)$  is a factor of $f(x)=x^3-6x^2+3x+10$ .

• TRUE

• FALSE

 If  $P(α)=0$ , then  $x−α$  is a factor of  $P(x)$ .

• TRUE

• FALSE

If  $𝑥−α$ is a factor of  $𝑃(𝑥)$ , then  $𝑃(α)=0$ 

.

• TRUE

• FALSE

If $βx+α$ is a factor of  $P(x)$ , then  $P\left(\frac{−α}{β}\right)=0$  .

• TRUE

• FALSE