Synthetic Division

Question 1

Express the remainder x and the quotient q, when y is divided by z

Answer 1

q+(x/z)

Quotient+(remainder/divisor)

Question 2

First thing to do when dividing a complicated polynomial by another, given the answer is a polynomial as well

Answer 2

1. choose a random number and plug it into the question

2. plug in the same numbers into the answer choices until the correct one is found

Question 3

Find the remainder of a polynomial a(x^2)+bx+c by x-q

Answer 3

The remainder theorem: plugging in the 0 of the divisor into the dividend would yield the remainder

1. Find the 0 of the divisor (in this case q)
2. Plug in q into the dividend=remainder

Question 4

Divisor’s relation to dividend given the remainder 0

Answer 4

The divisor is a factor of the dividend

Question 5

Given the remainder when a(x^2)+bx+c is divided x-q, what is the constant b given a, c and q

Answer 5

1. Find the 0 of divisor (in this case q)
2. Plug it into the dividend and set it equal to 0 (since the divisor is a factor) – in this case, a(q^2)+bq+c=0
3. Solve for b

Question 6

Given a table of values which correlates f(x) to x, where f(x)=0 when the value of x=q, find a factor of f(x)

Answer 6

Since f(x)=0 when q is plugged in, (x-q) (in other words: when one finds the 0 of x-q, one should be able to plug in that 0 into f(x) to find its 0)
.:. the answer is x-q