Remainder Theorem, Factor Theorem & Zeroes of the Polynomial

Find the remainder when

 $P\left(x\right)=x^4+x^3-2x^2+4x-5$  is divided by  $\left(x+3\right)$  .

• 19

• 20

• 21

• 22

Tags

CCSS.HSA.APR.B.2

Find the remainder when   $P\left(x\right)=2x^3+x^2-24x+36$  is divided by  $\left(2x+1\right)$ .

• 47

• 48

• 49

• 50

Determine if  $\left(x-1\right)$   is a factor of  $5x^4-2x^3+3x-6$  .

• Yes

• No

Tags

CCSS.HSA.APR.B.2

Determine if  $\left(2x-5\right)$  is a factor of  $4x^2-16x+15$  .

• Yes

• No

Determine if  $\left(x-1\right)$   is a factor of  $6x^3-2x^2+5x-8$  .

• Yes

• No

Tags

CCSS.HSA.APR.B.2

What can we say if  $P\left(-3\right)=0$  ?

•  $\left(x-3\right)\$  is a factor of  $P\left(x\right)$  

•  $\left(x+3\right)$  is a factor of  $P\left(x\right)$  

•  $\left(x-3\right)$  is NOT a factor of  $P\left(x\right)$  

Tags

CCSS.HSA.APR.B.2

What can we say if  $P\left(2\right)=3$  ?

•  $\left(x-2\right)$  is a factor of  $P\left(x\right)$  

•  $\left(x-2\right)$  is NOT a factor of  $P\left(x\right)$  

•  $\left(x+2\right)$  is NOT a factor of  $P\left(x\right)$  

Tags

CCSS.HSA.APR.B.2

Find the value of  $a$   if  $2x^3+x^2+a$  has a remainder  $-9$  when divided by  $x+2$   . 

• 1

• 2

• 3

• 4

Polynomial  $P\left(x\right)=ax^3-9x^2-25x+b$  is divisible by  $\left(x+1\right)$  and  $\left(x-4\right)$  .
Find the values of  $a$  and  $b$ .

•  $a=4\ \ ;\ \ b=12$  

•  $a=4\ ;\ \ b=-12$  

•  $a=-4\ \ ;\ \ b=-12$  

Polynomial $P\left(x\right)=2x^3+ax^2-x+b$  has a factor  $\left(x+1\right)$   and leaves a remainder 12 when divided by  $\left(x-3\right)$ . 
Find the values of  $a$  and  $b$ .

•  $a=-5\ \ ;\ \ b=6$  

•  $a=5\ \ ;\ \ b=6$  

•  $a=-5\ \ ;\ \ b=-6$