Question

Divided Polynomials

Answer 1

\[(x^{2}+3x+2)\div(x+2)\]

Answer 2

\[(y^2+7y+10)\div(y+5)\]

Answer 3

do you know how to factor (x^2 +3x+2)?

Answer 4

no i dont know how to do any of this :/

Answer 5

to factor x^2 + 3x + 2, you need to find two numbers that multiply to 2 (last term) and add to 3 (middle coefficient)

those two numbers are 1 and 2 since 1*2 = 2 and 1+2 = 3


This means x^2 + 3x + 2 factors to (x+1)(x+2)

Answer 6

so...

\[\large \frac{x^2+3x+2}{x+2}\]

\[\large \frac{(x+1)(x+2)}{x+2}\]

\[\large \frac{(x+1)\cancel{(x+2)}}{\cancel{x+2}}\]

\[\large x+1\]

Answer 7

so that would be your answer for the first one
x+1?

Answer 8

yep, you got it

Answer 9

so the idea is to

step 1) factor everything as much as possible

step 2) cancel the common factors

Answer 10

okay so can you break this one down for me please like you did the first one?
\[\frac{ 2x^4-13x^3+16x^2-9x+20 }{ x-5 }\]

Answer 11

you will have to use polynomial long division here

or synthetic division

Answer 12

idk how to do that can you do it step by step so i can see how to do it?

Answer 13

have you ever done polynomial long division before?

Answer 14

no sir!

Answer 15

hmm ok one sec

Answer 16

can you do the second question that i posted at the top ?

Answer 17

I recommend reading this lesson here

http://www.purplemath.com/modules/polydiv2.htm

Answer 18

what do you get when you factor y^2+7y+10

Answer 19

(y+1)(y+2)

Answer 20

no

Answer 21

you need to find two numbers that multiply to 10 and add to 7

Answer 22

there are no numbers?

Answer 23

you sure?

Answer 24

list the possible ways to factor 10 and see which pairs add to 7

Answer 25

5 and 2?

Answer 26

so it factors to (y+5)(y+2)

Answer 27

so your answer would be y+2?

Answer 28

yep

Answer 29

okay so now can you help me solve the one i posted like 5 mins ago up top the longer one?

Answer 30

\[(20x^3-8x^2+5x-5)\div(5x-2)\]

Answer 31

like I said, you use polynomial long division

I recommend reading that lesson