Question

Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

Part 1. Show all work using long division to divide your polynomial by the binomial.

Part 2. Show all work to evaluate f(a) using the function you created.

Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

Answer 1

my functions are (x^3 - 3x^2 - x + 3), and (x - 1).

Answer 2

long division hasnt change since the 3rd grade ....

Answer 3

@dan815
@Danielp
@marissalovescats

Answer 4

but it is using polynomials, just a tad harder

Answer 5

its exactly the same hardness as normal :/



--------------------
x - 1 | x^3 - 3x^2 - x + 3

how many times does x go into x^3?

Answer 6

3 times :P

Answer 7

x*x^2 = x^3 .... id say x^2 times

Answer 8

x*x=x^2 then x^2*x=x^3 ohhhhhhhh xD

Answer 9

x^2
--------------------
x - 1 | x^3 - 3x^2 - x + 3


now we mulitply, and subtract, and pull down whats left

x^2
--------------------
x - 1 | x^3 - 3x^2 - x + 3
-(x^3 - x^2)
------------
-2x^2 - x + 3

and repeat ... how many times does x go into -2x^2?

Answer 10

2 times?

Answer 11

almost :) x*-2x = -2x^2, lets go with -2x times

Answer 12

oooh i was debating whether -2 or 2...

Answer 13

x^2 - 2x
--------------------
x - 1 | x^3 - 3x^2 - x + 3


now we mulitply, and subtract, and pull down whats left

x^2 - 2x
--------------------
x - 1 | x^3 - 3x^2
-(x^3 - x^2)
------------
-2x^2 - x + 3
-(-2x^2+2x)
------------
-3x + 3


and repeat ... how many times does x go into -3x?

Answer 14

-3 times

Answer 15

yes, this time its just -3 :) -3*x = -3x soo what do we do?

Answer 16

divide by -3?

Answer 17

notice that we are simply playing with first terms such that:

x * k = x^3

k = x^3/x = x^2

or again

x * k = -2x^2

k = -2x^2/x = -2x

Answer 18

and no we dont divide by -3 ... we use it in the same way weve always used it when doing longhand division .... the same way i demonstrated the two times before

Answer 19

multply, and subtract ....

Answer 20

@amistre64 so do x-1*-3? im confused...

Answer 21

of course ...

Answer 22

mmk little confused spo was checking

Answer 23

so x*-3 is -3x and -1*-3=3

Answer 24

refresh with numbers if its been too long :)

00
-------
52 | 1245

124/52 = 2.xxx , use 2, 2(52) = 104


002
-------
52 | 1245
-104
----
205 , drop down the 5 and repeat ...

Answer 25

so 20*x-1

Answer 26

20x-20

Answer 27

not sure why youre going with 20 ...

-3(x-1) = -3x+3 .... then subtract it from the rest

Answer 28

oh you said drop the 5 so... oh

Answer 29

forgot something so reedit to include that -3 again :)

how many times does x go into -3x? -3 times soo


x^2 - 2x - 3
--------------------
x - 1 | x^3 - 3x^2 - x + 3


now we mulitply, and subtract, and pull down whats left

x^2 - 2x - 3
--------------------
x - 1 | x^3 - 3x^2
-(x^3 - x^2)
------------
-2x^2 - x + 3
-(-2x^2+2x)
------------
-3x + 3
-(-3x + 3)
---------
0, our remainder is simply zero now

Answer 30

so what would we do for part 2?

Answer 31

librarys closing so youre on your own ... or at least im on my own :) good luck

Answer 32

Oh ok thx