Long and Synthetic Division

Long Division

• Polynomial long division can be used to divide a polynomial d(x), producing a quotient polynomial q(x) and a remainder polynomial r(x)

Question 1

• Make sure the powers are in descending order!

• Divide Using Long Division

(

Question 2

• Divide Using Long Division(x

Question 3

• Divide Using Long Division

(

Question 4

• Divide Using long Division

(42 +

Question 5

• Use the Remainder Theorem to evaluate each function at the given value.

f(x) = 2

Question 6

• Use the Remainder Theorem to evaluate each function at the given value.

f(m) = at x=7

Question 7

• Find all the zeros. One zero has been given.

f(x)=

Question 8

Find all the zeros. One zero has been given.

• f(x)= 2

Question 9

Find all the zeros. One zero has been given.

• f(x)= 1

Question 10

Find all the zeros. One zero has been given.

• f(x)= 4

Question 11

Find all the zeros. One zero has been given.

• f(x)= -1

Question 12

• State the possible rational zeros for each function. Then find all rational zeros.

f(x)=

Question 13

• State the possible rational zeros for each function. Then find all rational zeros.

f(x)=4

Question 14

• State the possible rational zeros for each function. Then find all rational zeros.

f(x)=

Question 15

• Just list the possible rational zeros.

f(x)=5

Question 16

• What are rational and irrational numbers?

Question 17

• What type of zeros will not be included in the possible rational numbers list?

Question 18

• What are the two important things that the Remainder Theorem says?

Question 19

• What does it mean to have multiplicity of zeros?

Question 20

• How can you verify zeros of a polynomial using a graphing calculator?