Dividing Polynomials

What should be the order of the polynomial coefficients if

(3x - 4x³+ 6x⁴ + 1) is divided by (x + 3)?

• 3 0 -4 6 1

• 6 -4 3 1 0

• 6 -4 0 3 1

• -6 4 0 -3 -1

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.

Using long division, find the quotient of the polynomial (4x² - 24x + 35) when it is divided by (2x - 5).

• 2x - 7

• 2x - 12

• 2x + 12

• 2x + 7

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656
• p(2) = 652
• p(2) = -64
• p(2) = -368

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0
• 2
• 4
• 6

Is (x-4) a factor of (x³ +x² -16x-16)?

• YES
• NO

 $\left(3x^3-4x^2-x+1\right)\div\left(x+1\right)$  

A student is trying to use long division to solve the problem above.  What value should go in the box next?

• -2x

• 2x

• -7x

• 7x

 $f\left(x\right)=x^3+3x^2-6x-8$  

Using synthetic division, factor the function above given that (x+1) IS a factor.

• (x+1)(x-2)(x+4)

• (x+1)(x+2)(x-4)

• (x+1)(x-3)(x+2)

• (x+1)(x+3)(x-2)

Is this division problem worked correctly?

• This is correct!
• This is incorrect!

Using synthetic division, divide the polynomial

(2x³ + 4x² - 5) by (x + 3).

• 2x² + 2x - 4 R(-12)

• 2x² - 2x + 6 R(-23)

• 2x² - 2x + 8 R(-20)

• 2x² - 4x + 1 R0