Medal for right answer :)))))))))))
Find the remainder of (h^4 + h^2 – 2) ÷ (h + 3)

- anonymous

Medal for right answer :)))))))))))
Find the remainder of (h^4 + h^2 – 2) ÷ (h + 3)

- Stacey Warren - Expert brainly.com

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- schrodinger

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- Megatronprime

Here's what I found: H^4+h^2−2=h+3
Subtract h+3 from both sides.
h^4+h^2−2−(h+3)=h+3−(h+3)
h^4+h^2−h−5=0
Use quartic formula.
h=−1.227079,1.444794

- anonymous

I HAVE 4 MORE QUESTIONS AFTER THIS ONE :) lmao

- Nnesha

there are two ways to find remainder
1st) divide by using long or synthetic division method
2nd) solve the divisor `h+3` for the variable h and then substitute h for its value into the polynomial

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## More answers

- anonymous

how should i write that though like whats the final answer it says type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

- Michele_Laino

hint:
it is suffice to replace \(h=-3\) into this polynomial:
\(h^4+h^2-2\)

- anonymous

so what’s the final and complete answer :)??????????

- Michele_Laino

please try to do this computation:
\((-3)^4+(-3)^2-2=...?\)

- anonymous

88?

- Michele_Laino

that's right!

- anonymous

so thats the final answer?

- Michele_Laino

yes! We have applied the so called \(Theorem \;of\; Ruffini\)

- anonymous

I have more questions so more medals to give

- Nnesha

these kids should learn how to substitute numbers.

- anonymous

Using synthetic division, find (2x^4 + 4x^3 + 2x^2 + 8x + 8) ÷ (x + 2).

- anonymous

anyone??

- anonymous

thx btw

- Michele_Laino

I know how to do such division, nevertheless I have a slightly different method, since I'm italian

- anonymous

cool cool so????

- Michele_Laino

if you want I can apply my method

- anonymous

yeah i just need the answer :)

- Michele_Laino

I'm sorry, I can't give the direct answer, since it is against the Code of Conduct

- anonymous

well just make it more simple

- Michele_Laino

ok!
first step we have to make such division: \(2x^4:x=...?\)

- anonymous

2^3

- anonymous

so is it 2x^3+2x^2 or just 2x?

- Michele_Laino

we have \(2x^3\) am I right?

- anonymous

yeah?

- anonymous

but the ned number? is it 2x?

- anonymous

next*

- Michele_Laino

so we can write this:
|dw:1450290685256:dw|

- anonymous

wait so whats next?

- Michele_Laino

next we have to do this computation:
\[ - 2{x^3}\left( {x + 2} \right) = ...?\]

- anonymous

is the answer 2x^3+2x^2+4

- Michele_Laino

yes! It is

- anonymous

yaws

- anonymous

wait a sec

- anonymous

k so theres a triangle so 3 sides

- anonymous

one side is A=2c^3+16

- anonymous

b=c+2

- anonymous

so what is the height or h

- anonymous

?/////????

- Michele_Laino

we have to compute the area of such triangle, first

- anonymous

Hint: The formula for area of a triangle is A = bh, where b is the length of the base and h is the height of the triangle.)

- Michele_Laino

yes! I know, nevertheless, we have to use the Eron's formula first

- anonymous

oaky

- anonymous

sry I’m pretty bad at this

- Michele_Laino

firs step, we have to compute the half perimeter:
\(p=(a+b+c)/2=(2c^3+16+c+2+c)/2=...?\)

- Michele_Laino

first*

- anonymous

okay

- Michele_Laino

please try to complete such computation

- anonymous

is it 2c^2-4c+8? theres also another one which ends with some more numbers

- anonymous

like after 8 theres ((32/c+2))

- anonymous

so which is it

- Michele_Laino

hint:
the perimeter is:
\[\begin{gathered}
\left( {2{c^3} + 16} \right) + \left( {c + 2} \right) + c = 2{c^3} + 2c + 18 = \hfill \\
\hfill \\
= 2\left( {{c^3} + c + 9} \right) \hfill \\
\end{gathered} \]
so, what is the half-perimeter?

- anonymous

I’m not sure? does the answer not start with 2c^2 is it maybe 4c^2

- Michele_Laino

it is not the answer it is the perimeter

- anonymous

so what’s the height? I’m confused

- Michele_Laino

as you well know, a triangle has three heights

- Michele_Laino

is the triangle a right triangle?

- anonymous

what but i know a and b so whats c

- anonymous

right?

- Michele_Laino

like this one:
|dw:1450291781898:dw|

- anonymous

the h that I’m trying to find is a 90 degree

- anonymous

the one to the left

- Michele_Laino

please can you make a drawing of the triangle?

- anonymous

yeah wait

- anonymous

##### 1 Attachment

- anonymous

there it is

- Michele_Laino

is \(A\) an area?

- anonymous

what

- anonymous

I’m trying to find h

- anonymous

Find the height, h, of the triangle shown.
h = .
(Hint: The formula for area of a triangle is A = bh, where b is the length of the base and h is the height of the triangle.)

- Michele_Laino

then we have to solve such equation:
\((c+2) \ h=2c^3+16\)

- anonymous

if i give you 4 options can u tell me which on is correct

- Michele_Laino

namely we have to find the value of \(h\):
\[h = \frac{{2{c^3} + 16}}{{c + 2}} = ...?\]

- anonymous

here are the answer options

##### 1 Attachment

- anonymous

is it a b c or d??????????

- anonymous

plzzzzzz

- Michele_Laino

hint:
we can use this identity:
\[\begin{gathered}
2{c^3} + 16 = 2\left( {{c^3} + 8} \right) = \hfill \\
\hfill \\
= 2\left( {c + 2} \right)\left( {{c^2} - 2c + 4} \right) \hfill \\
\end{gathered} \]
so, after a substitution, we get:
\[h = \frac{{2{c^3} + 16}}{{c + 2}} = \frac{{2\left( {c + 2} \right)\left( {{c^2} - 2c + 4} \right)}}{{c + 2}} = ...?\]

- anonymous

ok so the answer is 2c^2-4c+8?

- Michele_Laino

that's right!

- anonymous

ok thanks! another one lmao

- anonymous

Using synthetic division, find (2x4 − 3x3 − 20x − 21) ÷ (x − 3).

- Nnesha

forget about the answer for a sec
learn how it works
all 3 questions are about login/synthetic division and you have no idea how to do that

- Nnesha

long***

- anonymous

##### 1 Attachment

- anonymous

i’m sorry math isn’t my strong suit can u not

- Michele_Laino

as I wrote before I can help you using my method

- anonymous

okay? so

- anonymous

Using synthetic division, find (2x^4 − 3x^3 − 20x − 21) ÷ (x − 3).

- Nnesha

i can understand but you're not trying at all answers not gonna help you
how about learn the method and do the rest of them by ur own
save ur time

- Michele_Laino

first step, we have to do this division:
\(2x^3:x=...?\)

- Michele_Laino

oops.. \(\large 2x^4:x=...?\)

- anonymous

i’m good thanks

- anonymous

2x^3?

- anonymous

i already know that though

- anonymous

isn’t this the answer?

##### 1 Attachment

- Michele_Laino

that's right! So I can make this drawing:
|dw:1450292651408:dw|

- anonymous

it makes sense

- anonymous

|dw:1450292784835:dw|

- anonymous

is this the answer?

- anonymous

or nah

- Michele_Laino

next we have to do this computation:
\[ - 2{x^3}\left( {x - 3} \right) = ...?\]

- anonymous

-2x^4+6x^3?

- anonymous

so i take it that my answer wasn’t right

- Michele_Laino

right! So I update my drawing like below:
|dw:1450292850022:dw|

- Michele_Laino

I have made the algebraic sum

- anonymous

is the answer 2x^3+3x^2-11x-54

- Michele_Laino

next, we have to do this computation:
\[\Large 3{x^3}:x=...?\]

- anonymous

so it’s 2x^3+3x^2+9x+7x?

- Michele_Laino

no, I'm sorry it is a wrong result

- anonymous

or is it 9x^2?

- Michele_Laino

please let's continue my computation

- anonymous

okay

- Michele_Laino

so, what is:
\[\Large 3{x^3}:x=...?\]

- anonymous

3x^2

- Michele_Laino

right! Now I update my drawing:
|dw:1450293169679:dw|

- Michele_Laino

next, we have to do such computation:
\[\Large - 3{x^2}\left( {x - 3} \right) = ...?\]

- anonymous

\[2x^3+3x^2-11x-54/x-3\]

- anonymous

is this it?

- Michele_Laino

no, I'm sorry

- anonymous

is it at least close to that?

- anonymous

i have 4 options one of them must be right

- Michele_Laino

please what is:
\[ - 3{x^2}\left( {x - 3} \right) = ...?\]

- anonymous

-3x^3+9x^2

- anonymous

this it?

##### 1 Attachment

- Michele_Laino

perfect! So I update my drawing like this:
|dw:1450293421363:dw|
again, I have made the algebraic sum

- anonymous

ok so its 2x^4+3x^3+9x^2+7x????????

- Michele_Laino

next, please what is:
\[\huge 9{x^2}:x = ...?\]

- anonymous

9x?

- Michele_Laino

that's right So we have this drawing:
|dw:1450293608851:dw|
now what is:
\[\huge - 9x\left( {x - 3} \right) = ...?\]

- anonymous

1/x^3

- anonymous

are we getting to the answer yet

- Michele_Laino

yes!
it is a multiplication: \[ \huge - 9x\left( {x - 3} \right) = ...?\]

- anonymous

so whats the final answer

- Michele_Laino

please can you make such computation?

- anonymous

2x^3+3x^2+9x+7x?

- Michele_Laino

no, I'm sorry

- anonymous

which one is it omfg

- Michele_Laino

please continue my computation, we are close to the end

- anonymous

this??????

##### 1 Attachment

- anonymous

right?

- Michele_Laino

no, I'm sorry:
\[ - 9x\left( {x - 3} \right) = ...?\]

- anonymous

-9x3

- Michele_Laino

it is \(-9x^3+27x\) am I right?

- anonymous

this must be it

##### 1 Attachment

- anonymous

dude is it a b c or d you’ve said no to all of them so which on is it

##### 1 Attachment

- Michele_Laino

so I update my drawing like below:
|dw:1450293966061:dw|
oops... it is \(-9x^2+27x\)

- anonymous

what

- Michele_Laino

finally:
what is:
\[\huge 7x:x\]

- anonymous

7

- anonymous

so this is it

##### 1 Attachment

- Michele_Laino

that's right! So we have:
|dw:1450294116676:dw|
then we have to compute this:
\(-7(x-3)=...?\)

- anonymous

okay so last one

- anonymous

Using synthetic division, find (x^4 − 2) ÷ (x + 1).

- anonymous

##### 1 Attachment

- Michele_Laino

here we have to apply the same procedure as before

- anonymous

i haven’t really mastered that

- anonymous

so what is it

- Michele_Laino

please if you are patient, I guide you through the final answer, as in previous exercise, otherwise I can't do nothing, since I have to respect the Code of Conduct

- anonymous

okay thats fine

- Michele_Laino

ok!
Now, first step:
we have to do this computation:
\(x^4:x=...?\)

- anonymous

x^3

- Michele_Laino

right! So I can make this drawing:
|dw:1450294494695:dw|

- anonymous

yeah

- Michele_Laino

next, what is:
\(-x^3(x+1)=...?\)

- anonymous

-x^4=x^3

- anonymous

i meant - not =

- Michele_Laino

correct! So I update my drawing loke below:
|dw:1450294645933:dw|
I have made the algebraic sum
now, what is:
\(-x^3:x=...?\)

- anonymous

-x^2

- Michele_Laino

perfect! So I have this:
|dw:1450294775213:dw|
now, what is \(x^2(x+1)=...?\)

- anonymous

is this the answer though

##### 1 Attachment

- Michele_Laino

I don't know, since I did not such division

- anonymous

x^3+x^2

- Michele_Laino

ok! I update my drawing:
|dw:1450294916258:dw|
next, what is \(x^2:x=...?\)

- anonymous

x

- Michele_Laino

ok1 So we have:
|dw:1450295005204:dw|
then, what is \(-x(x+1)=...?\)

- Michele_Laino

oops.. I meant ok!

- anonymous

x+1 sry I’m not sure

- Michele_Laino

it is a multiplication, so we can write this:
\(-x(x+1)=-x\cdot x-x\cdot 1=...?\)

- anonymous

ok?

- Michele_Laino

it is \(-x^2-x\) am I right?

- anonymous

yeah i think so

- Michele_Laino

then, I update again my drawing:
|dw:1450295269730:dw|
now, what is \(-x:x=...?\)

- anonymous

-1

- Michele_Laino

correct! So, I can write this:
|dw:1450295356053:dw|
finally, what is \(1 \cdot (x+1)=...?\)

- anonymous

x+1?

- anonymous

what is it

- anonymous

I’m a little confused so which on is it exactly?

##### 1 Attachment

- Michele_Laino

perfect, so we can write:
|dw:1450295455934:dw|
we have finished, since the remainder is a number which is a zero grade polynomial, namely its grade is less the grade of the polynomial divisor (x+1)
as we can see the quotient is \(x^3-x^2+x-1\) and the remainder is \(-1\)

- anonymous

is it a b c or d?

- anonymous

is this it

##### 1 Attachment

- Michele_Laino

so, we can write this:
\[\left( {{x^4} - 2} \right):\left( {x + 1} \right) = {x^3} - {x^2} + x - 1 - \frac{1}{{x + 1}}\]

- Michele_Laino

so, what is the right option?

- anonymous

so this is it

##### 1 Attachment

- Michele_Laino

that's right!

- anonymous

?

- Michele_Laino

yes! It is option A

- anonymous

YOURE A flutterING MORON I ONLY GOT 2 QUESTIONS RIGHT

- anonymous

WHAT THE ACTUAL flutter

- anonymous

YOU R SO SLOW I WASTED LIKE 3 HOURS ON YOU

- anonymous

EVERYTHING WAS WRONG WTF

- anonymous

OMFG SO DONE

- anonymous

TAKING THE MEDAL BACK

- anonymous

GO flutterING KILL YOURSELF feather

- Michele_Laino

you don't wasted your time, you took your time to master the synthetic division

- Nnesha

watch your language. plz refrain from offensive language &be respectful.

- Nnesha

synthetic division is easy
\[\rm (2x^4-3x^3-20x-21) \div (x+3)\]
divisor is x+3 set it equal to 0 \[x+3=0\]
to cancel out 3 from left side you should do opposite of `addition` which is subtraction
so subtract 3 both sides
you will get `x=-3`
now just write all coefficients of the polynomial |dw:1450297254123:dw|
i wrote 0 for 0x^2
eventhough there is not x^2 terms but we have to write all terms from highest degree to lowest
so x^4,x^3,x^2,x^1,x^0

- Nnesha

carry down the leading coefficient first number |dw:1450297579766:dw|
and then multiply by -3 write the answer above the line and then add the two numbers in the 2nd column

- Nnesha

|dw:1450297743314:dw|
and thne repeat the pattern
multiply by -3 write the answer above the line and then add both numbers in the 3rd column

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