1. What could be the remaining factors of 16x^5-32x^4-81x+162 if x-2 is one of them?

2. The volume of a fudge tin meust be 120 cm^3. The tin is 7cm longer than it is wide and six times longer than it is tall. Find the dimenmsions of the tin

Question

1. What could be the remaining factors of 16x^5-32x^4-81x+162 if x-2 is one of them?

2. The volume of a fudge tin meust be 120 cm^3. The tin is 7cm longer than it is wide and six times longer than it is tall. Find the dimenmsions of the tin

anonymous · Answer

16x^4(x-2)-81(x-2)
factor out x-2

anonymous · Answer

how did you do that?
did you have a formula
can u give me the formula

anonymous · Answer

plzzz
i need some help

anonymous · Answer

getting there be patient

anonymous · Answer

ok

anonymous · Answer

okay so we just grouped the like terms $$\color {red}{16x^5-32x^4}-\color{blue}{81x-162}$$

anonymous · Answer

for red factor 16x^4x
for blue factor -81x
this is called grouping

anonymous · Answer

if you remove x-2 from the first group you get (x-2)(16x^4) and if you remove x-2 from the second group you get (x-2)(-81) therefore you now have (x-2)(16x^4)+(x-2)(-81) can you simplify it from there?

anonymous · Answer

16x^5-32x^4-81x+162

anonymous · Answer

x=2

anonymous · Answer

no you are expanding it again. you are looking for the other root.
take this equation 
(x−2)(16x^4)+(x−2)(−81)
 and do this to it
(x−2)(16x^4−81)

made an error in the last post forgive me.

anonymous · Answer

now seeing as you have the root x-2 and another equation 16x^4-81 you now need to simplify the second equation.

anonymous · Answer

1.5

anonymous · Answer

huh? now you lost me. find the roots of (16x^4-81)

anonymous · Answer

??????

anonymous · Answer

what grade are you in and what is the purpose of this question?

anonymous · Answer

we have to look for the remaining factors......
we don't have to find the zeroes of the function

anonymous · Answer

i know this. he answer to your question i cannot just give you so i am giving you the steps. I am not giving you the zeros.

anonymous · Answer

ok........
sorry because i'm just condused

anonymous · Answer

simplify by removing x-2 
$$16x^{5}-32x^{4}-81x+162$$ you get$$(x-2)(16x^4)+(x-2)(-81)$$ then group the common factors like so$$(x-2)(16x^{4}-81)$$now find the factors of $$(16x^{4}-81)$$ by using the completing the square method of (a+b)(a-b)

anonymous · Answer

you follow so far?

anonymous · Answer

16x^4-81+6561

anonymous · Answer

no simplify it thus $$(4x^{2})^{2}-9^{2}$$ you get $$(4x^{2}-9)(4x^{2}+9)$$ now simplify $$(4x^2-9)$$ again to get $$(2x-3)(2x+3)$$ therefore your roots are $$(x-2)(2x+3)(2x-3)(4x^2+9)$$ Do you understand this?

anonymous · Answer

wait

anonymous · Answer

my answer is wrong.....
hahahaha

anonymous · Answer

what do you mean?

anonymous · Answer

i'll just understand this steps

anonymous · Answer

what do you mean by this "my answer is wrong.....
hahahaha"?

anonymous · Answer

i'm solving right here on my seat with a paper and calculator

anonymous · Answer

you are a bit funny @kris10

anonymous · Answer

are you doing it the way i showed you?

anonymous · Answer

hehehe yeah but i got the wrong one. . . 
the wrong answer

anonymous · Answer

@Jonask :D

anonymous · Answer

thanks for the both of you 
can you help me with the 2nd question?

anonymous · Answer

2. The volume of a fudge tin meust be 120 cm^3. The tin is 7cm longer than it is wide and six times longer than it is tall. Find the dimenmsions of the tin

anonymous · Answer

will do

anonymous · Answer

basically yu have to create an equation for the tin so draw a rectangle for me.

anonymous · Answer

|dw:1360032254784:dw|

anonymous · Answer

then

anonymous · Answer

now what will the longest side be?

anonymous · Answer

length
and the shorter side is the width

anonymous · Answer

if we make the width Xcm what will the width be?

anonymous · Answer

huh? i don't understand anything. . .

anonymous · Answer

look at this diagram|dw:1359974978458:dw|