Introduction to Synthetic Division of Polynomials

What does this tell me?

• f(-2)= -27 and -27 is the remainder

• -2 is a solution of the function

• (x+2) is a factor of the function

• (x-2) is a factor of the function

How can I tell, when doing synthetic division, if the binomial is a FACTOR of the dividend?

• The remainder is zero

• They are all factors

• We can't tell

• The remainder is a constant

If x-2 is a factor of x^2+5x+7, then that means.....

• f(0) = 2

• f(0) = -2

• f(2) = 0

• f(-2) = 0

When can we use Synthetic Division to divide polynomials?

• Any time we need to divide.

• When dividing by a binomial

• When dividing by a trinomial

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

• 3   0   -4   6   1
• 6   -4   3   1   0
• 6   -4   0   3   1
• -6   4   0   -3   -1

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

• 0

• 1

• 2

• 3

            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. 

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division. This means, what is the remainder.

• 0

• 10

• 15

• -7

Let f(x) = 4x^2 -33x -27.  Is k = 9 a zero of the function?

• yes
• no

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