Question

Using synthetic division, what is the quotient: (3x3 + 4x - 32) ÷ (x - 2)?

3x2 + 6x - 16

3x2 - 6x + 16

3x2 + 6x + 16

3x2 - 6x - 16 + 1 over the quantity of x minus 2

Answer 1

can you show your work?

Answer 2

ok \[3x ^{3}\div x=2x ^{2}\]\[32\div2=16\]

Answer 3

\[4x \div x= 3x\]

Answer 4

@amistre64

Answer 5

that kinda looks like you are attempting a long hand division .... which is fine to get an option with

Answer 6

my strategy is this:

(3x3 + 4x - 32) ÷ (x - 2)
^^^^
this equals 0 when x=2



now make sure ALL the "x" parts are present

3 2 1 0
3x3 + 4x - 32


we are missing an x^2 part, fill it in with 0x^2

3 2 1 0
3x3 +0x2 + 4x - 32


now we can run thru the synthetic method

Answer 7

ok i follow so far

Answer 8

i use 3 rows like this

3x3 +0x2 + 4x - 32
0 <-- add this row down
--------------------
2 ) <-- multiply this row to move across, using the 2
as the multiplier

Answer 9

ok

Answer 10

3x3 +0x2 + 4x - 32
0
--------------------
2 ) 3


3*2 = 6, so plug it in and add down


3x3 +0x2 + 4x - 32
0 6
--------------------
2 ) 3 6 16


2*6 = 12, so plug it in and add down


3x3 +0x2 + 4x - 32
0 6 12
--------------------
2 ) 3 6 16


what would the next step be? its very repetitive

Answer 11

you would plug 16 in and add it to 32?

Answer 12

2 times 16, then add that result to -32

Answer 13

ok so it would get 0 on the end

Answer 14

yes, now we can see the parts:

3x3 +0x2 + 4x - 32
0 6 12 16
--------------------
2 ) 3 6 16 0
^______________^ ^remainder
quotient


and this is why i keep the x parts in place, they remind me how to rework the quotient ...


3x3 +0x2 + 4x - 32
0 6 12 16
--------------------
2 ) 3 6 16 0
x^2 x^1 x^0

3x^2 +6x +16

Answer 15

thank you so much man i have been stuck on this for a day

Answer 16

youre welcome :)