Question

1. Create your own third degree polynomial that when divided by x + 2 has a remainder of –4.


2. Create your own division of polynomials problem. Demonstrate how this problem would be solved using both long division and synthetic division.

Answer 1

what is the degree if you multiply x^2*(x+2) ?

Answer 2

\[\huge x^2(x+2) = \]

Answer 3

just multiply it out...

Answer 4

not quite...
\[\large x^2(x+2)=x^3+2x \]... agreed?

Answer 5

yes

Answer 6

so that's a third degree polynomial.. and what is the remainder if we take
\(\large x^3+2x \) divided by \(\large x+2 \) ???

Answer 7

remember we just multiplied it out to get that third degree polynomial...

Answer 8

-4

Answer 9

no...

Answer 10

confused...................

Answer 11

if I ask you to multipl 2 times 3, what's the product?

Answer 12

**multiply...

Answer 13

6

Answer 14

now... what's the remainder if I ask you 6 divided by 3 ?

Answer 15

0

Answer 16

that's what i was asking in when we were working with the polynomial x^3 + 2x...
the remainder when \(\large x^3+2x \) divided by \(\large x+2 \) is zero....

Answer 17

still with me?

Answer 18

yeah

Answer 19

good... but we want a remainder of -4....
so what do you think we need to do?

Answer 20

not sure