Remainder Theorem and Factor Theorem

What is the remainder when

 $\left(5x^2+14x-24\right)$  is divided by  $\left(x+4\right)$  ?

• 0

• 1

• 2
  

• 3

Which expression gives the remainder when

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

• P(-5)

• P(-2)

• P(2)

• P(5/4)

What is the remainder when  $\left(5x^{100}+5\right)$  is divided by  $\left(x-1\right)$  ?

• 5

• -5

• 10
  

• -10
  

Which of the following polynomials is exactly divisible by  $\left(3x+1\right)$  ?

•  $6x^2+17x+5$  
  

•  $9x^2+6x+1$  
  

•  $3x^3+4x^2-8x-3$  
  

• All of the above
  

If P(-2) = 0, which of the following statements is true about P(x)?

• x + 2 is a factor of P(x)

• 2 is a root of P(x) = 0

• P(x) = 0, has two negative roots

• P(0) = -2

Given  $P\left(x\right)=2x^3+3x^2-5x-12$  . What is the value of P(3)?

• 56

• 55

• 54

• 53

Genber will evaluate an 8th degree polynomial in x at x = 10 using the Remainder Theorem and Synthetic Division. How many coefficients of x will be written in the first row of the synthetic division procedure?

• 8

• 9

• 10

• 11

Find the value of k for which the binomial

 $\left(x+4\right)$  is a factor of $x^4+kx_{ }^3-4x^2$  .

• 1
  

• 2
  

• 3
  

• 4
  

Find the remainder when  $P\left(x\right)=2x^4+5x^3+2x^2-7x-15$  divided by  $\left(2x-3\right)$  

• 5
  

• 6

• 7

• 8

Which example correctly illustrates the factor theorem?

• $P\left(x\right)=2x^3-5x^2+4x-1;\ p=0,\ so\ x+1\ is\ a\ factor\ of\ P\left(x\right)$

• $P\left(x\right)=2x^3-5x^2+4x-1;\ P\left(1\right)\ =\ 0,\ so\ x+1\ is\ a\ factor\ of\ P\left(x\right)$
  

• $P\left(x\right)=2x^3-5x^2+4x-1;\ P\left(2\right),\ so\ x-2\ is\ a\ factor\ of\ P\left(x\right)$
  

• $P\left(x\right)=2x^3-5x^2+4x-1;\ x-1\ is\ a\ factor\ of\ P\left(x\right),\ so\ p\left(1\right)\ =\ -1$