Understanding zeroes and factors of polynomials

Which function has a remainder of 3 when divided by x+2?

• f(x) = x² - 6x +11
• f(x) = x² + 3x +5
• f(x) = x² - 4x +7
• f(x) = x² + 6x +5

If 𝒙²−𝟓 is divided by 𝒙−𝟐, then what is the remainder?

• 1

• -1

• 9

• 0

• 360

• 180

• 90

• 45

Mathematical Equivalence

ON

 $f\left(x\right)=4x^3+10x^2-6x-20$  
If (x+2) if a factor of the polynomial function above, then what is the remainder?

• -40

• 2

• 0

• 20

Given that $P\left(-2\right)=1,\ P\left(-1\right)=3,\ P\left(1\right)=0,\ P\left(2\right)=4$  

Find the remainder when P(x) is divided by x+2

If x²+3x+7 is divided by x+2, then what is the remainder?

• 0

• -3

• 9

• 5

What is the remainder when dividing (x³ - 3x² - 10x + 24) by x+3?

• -4

• 8

• 0

• 3

 $\left(x+1\right)$  is a factor of which 3 polynomials below.  There are 3 answers.  Try using the Remainder Theorem to see which polynomial has a remainder of zero.  

•  $p\left(x\right)=x^3-7x^2-11x-3$  

•  $P\left(x\right)=x^2+10x-5$  

•  $P\left(x\right)=x^3+x^2+9x+9$  

•  $p\left(x\right)=x^4+3x^2-4$