2.1 Dividing Polynomials and Remainder Theorem

(2x³ + 5x² + 9) ÷ (x + 3)

• 2x² - x + 3
• 2x³ - x² + 3x
• 2x² + 11x + 33 + 108/x+3
• 2x² - 5x + 12

For synthetic division, what would be the number in the left hand box?

• 0
• 1
• 2
• 3

Is this division problem worked correctly?

• This is correct!
• This is incorrect!

            Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.
• No, (x-2) is  not a factor. The remainder is zero.
• Yes, (x-2) is a factor. The remainder is zero.
• No, (x-2) is  not a factor. There is a remainder. 

 $\left(x^3+6x^2+11x+16\right)\div\left(x+1\right)$  

•  $x^2+5x+16$  

•  $x^{2\ }+5x+6+\frac{10}{x+1}$  

•  $x^{2\ }+5x+6+\frac{10}{x^3+6x^2+11x+16}$  

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0
• 2x-10
• -2x-10
• 2x+10

The expression x³ ─ kx² +2x +5 leaves a remainder of 2 when divided by x ─ 3. Find the value of k.

• 4

• -4

• 8

The area of a rectangular pool table is: x² + 14x +40.

The length is x + 4. What is the width?

• x + 8

• x + 14

• x + 10

• x +4

Is this division problem worked correctly?

• This is correct!

• This is incorrect, and error occurs when subtracting -6x and 2x

  and it is carried out in the process

• This is incorrect, and the error occurs on the 4th line!

• This is incorrect, and the error occurs on the 3rd line!

Identify the missing term to complete the solution.

• 4

• -4

• 5

• -5