anonymous
  • anonymous
Medal for right answer :))))))))))) Find the remainder of (h^4 + h^2 – 2) ÷ (h + 3)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Megatronprime
  • 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
  • anonymous
I HAVE 4 MORE QUESTIONS AFTER THIS ONE :) lmao
Nnesha
  • 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • 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
  • Michele_Laino
hint: it is suffice to replace \(h=-3\) into this polynomial: \(h^4+h^2-2\)
anonymous
  • anonymous
so what’s the final and complete answer :)??????????
Michele_Laino
  • Michele_Laino
please try to do this computation: \((-3)^4+(-3)^2-2=...?\)
anonymous
  • anonymous
88?
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
so thats the final answer?
Michele_Laino
  • Michele_Laino
yes! We have applied the so called \(Theorem \;of\; Ruffini\)
anonymous
  • anonymous
I have more questions so more medals to give
Nnesha
  • Nnesha
these kids should learn how to substitute numbers.
anonymous
  • anonymous
Using synthetic division, find (2x^4 + 4x^3 + 2x^2 + 8x + 8) ÷ (x + 2).
anonymous
  • anonymous
anyone??
anonymous
  • anonymous
thx btw
Michele_Laino
  • Michele_Laino
I know how to do such division, nevertheless I have a slightly different method, since I'm italian
anonymous
  • anonymous
cool cool so????
Michele_Laino
  • Michele_Laino
if you want I can apply my method
anonymous
  • anonymous
yeah i just need the answer :)
Michele_Laino
  • Michele_Laino
I'm sorry, I can't give the direct answer, since it is against the Code of Conduct
anonymous
  • anonymous
well just make it more simple
Michele_Laino
  • Michele_Laino
ok! first step we have to make such division: \(2x^4:x=...?\)
anonymous
  • anonymous
2^3
anonymous
  • anonymous
so is it 2x^3+2x^2 or just 2x?
Michele_Laino
  • Michele_Laino
we have \(2x^3\) am I right?
anonymous
  • anonymous
yeah?
anonymous
  • anonymous
but the ned number? is it 2x?
anonymous
  • anonymous
next*
Michele_Laino
  • Michele_Laino
so we can write this: |dw:1450290685256:dw|
anonymous
  • anonymous
wait so whats next?
Michele_Laino
  • Michele_Laino
next we have to do this computation: \[ - 2{x^3}\left( {x + 2} \right) = ...?\]
anonymous
  • anonymous
is the answer 2x^3+2x^2+4
Michele_Laino
  • Michele_Laino
yes! It is
anonymous
  • anonymous
yaws
anonymous
  • anonymous
wait a sec
anonymous
  • anonymous
k so theres a triangle so 3 sides
anonymous
  • anonymous
one side is A=2c^3+16
anonymous
  • anonymous
b=c+2
anonymous
  • anonymous
so what is the height or h
anonymous
  • anonymous
?/////????
Michele_Laino
  • Michele_Laino
we have to compute the area of such triangle, first
anonymous
  • 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
  • Michele_Laino
yes! I know, nevertheless, we have to use the Eron's formula first
anonymous
  • anonymous
oaky
anonymous
  • anonymous
sry I’m pretty bad at this
Michele_Laino
  • 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
  • Michele_Laino
first*
anonymous
  • anonymous
okay
Michele_Laino
  • Michele_Laino
please try to complete such computation
anonymous
  • anonymous
is it 2c^2-4c+8? theres also another one which ends with some more numbers
anonymous
  • anonymous
like after 8 theres ((32/c+2))
anonymous
  • anonymous
so which is it
Michele_Laino
  • 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
  • anonymous
I’m not sure? does the answer not start with 2c^2 is it maybe 4c^2
Michele_Laino
  • Michele_Laino
it is not the answer it is the perimeter
anonymous
  • anonymous
so what’s the height? I’m confused
Michele_Laino
  • Michele_Laino
as you well know, a triangle has three heights
Michele_Laino
  • Michele_Laino
is the triangle a right triangle?
anonymous
  • anonymous
what but i know a and b so whats c
anonymous
  • anonymous
right?
Michele_Laino
  • Michele_Laino
like this one: |dw:1450291781898:dw|
anonymous
  • anonymous
the h that I’m trying to find is a 90 degree
anonymous
  • anonymous
the one to the left
Michele_Laino
  • Michele_Laino
please can you make a drawing of the triangle?
anonymous
  • anonymous
yeah wait
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
there it is
Michele_Laino
  • Michele_Laino
is \(A\) an area?
anonymous
  • anonymous
what
anonymous
  • anonymous
I’m trying to find h
anonymous
  • 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
  • Michele_Laino
then we have to solve such equation: \((c+2) \ h=2c^3+16\)
anonymous
  • anonymous
if i give you 4 options can u tell me which on is correct
Michele_Laino
  • Michele_Laino
namely we have to find the value of \(h\): \[h = \frac{{2{c^3} + 16}}{{c + 2}} = ...?\]
anonymous
  • anonymous
here are the answer options
anonymous
  • anonymous
is it a b c or d??????????
anonymous
  • anonymous
plzzzzzz
Michele_Laino
  • 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
  • anonymous
ok so the answer is 2c^2-4c+8?
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
ok thanks! another one lmao
anonymous
  • anonymous
Using synthetic division, find (2x4 − 3x3 − 20x − 21) ÷ (x − 3).
Nnesha
  • 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
  • Nnesha
long***
anonymous
  • anonymous
anonymous
  • anonymous
i’m sorry math isn’t my strong suit can u not
Michele_Laino
  • Michele_Laino
as I wrote before I can help you using my method
anonymous
  • anonymous
okay? so
anonymous
  • anonymous
Using synthetic division, find (2x^4 − 3x^3 − 20x − 21) ÷ (x − 3).
Nnesha
  • 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
  • Michele_Laino
first step, we have to do this division: \(2x^3:x=...?\)
Michele_Laino
  • Michele_Laino
oops.. \(\large 2x^4:x=...?\)
anonymous
  • anonymous
i’m good thanks
anonymous
  • anonymous
2x^3?
anonymous
  • anonymous
i already know that though
anonymous
  • anonymous
isn’t this the answer?
Michele_Laino
  • Michele_Laino
that's right! So I can make this drawing: |dw:1450292651408:dw|
anonymous
  • anonymous
it makes sense
anonymous
  • anonymous
|dw:1450292784835:dw|
anonymous
  • anonymous
is this the answer?
anonymous
  • anonymous
or nah
Michele_Laino
  • Michele_Laino
next we have to do this computation: \[ - 2{x^3}\left( {x - 3} \right) = ...?\]
anonymous
  • anonymous
-2x^4+6x^3?
anonymous
  • anonymous
so i take it that my answer wasn’t right
Michele_Laino
  • Michele_Laino
right! So I update my drawing like below: |dw:1450292850022:dw|
Michele_Laino
  • Michele_Laino
I have made the algebraic sum
anonymous
  • anonymous
is the answer 2x^3+3x^2-11x-54
Michele_Laino
  • Michele_Laino
next, we have to do this computation: \[\Large 3{x^3}:x=...?\]
anonymous
  • anonymous
so it’s 2x^3+3x^2+9x+7x?
Michele_Laino
  • Michele_Laino
no, I'm sorry it is a wrong result
anonymous
  • anonymous
or is it 9x^2?
Michele_Laino
  • Michele_Laino
please let's continue my computation
anonymous
  • anonymous
okay
Michele_Laino
  • Michele_Laino
so, what is: \[\Large 3{x^3}:x=...?\]
anonymous
  • anonymous
3x^2
Michele_Laino
  • Michele_Laino
right! Now I update my drawing: |dw:1450293169679:dw|
Michele_Laino
  • Michele_Laino
next, we have to do such computation: \[\Large - 3{x^2}\left( {x - 3} \right) = ...?\]
anonymous
  • anonymous
\[2x^3+3x^2-11x-54/x-3\]
anonymous
  • anonymous
is this it?
Michele_Laino
  • Michele_Laino
no, I'm sorry
anonymous
  • anonymous
is it at least close to that?
anonymous
  • anonymous
i have 4 options one of them must be right
Michele_Laino
  • Michele_Laino
please what is: \[ - 3{x^2}\left( {x - 3} \right) = ...?\]
anonymous
  • anonymous
-3x^3+9x^2
anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
perfect! So I update my drawing like this: |dw:1450293421363:dw| again, I have made the algebraic sum
anonymous
  • anonymous
ok so its 2x^4+3x^3+9x^2+7x????????
Michele_Laino
  • Michele_Laino
next, please what is: \[\huge 9{x^2}:x = ...?\]
anonymous
  • anonymous
9x?
Michele_Laino
  • Michele_Laino
that's right So we have this drawing: |dw:1450293608851:dw| now what is: \[\huge - 9x\left( {x - 3} \right) = ...?\]
anonymous
  • anonymous
1/x^3
anonymous
  • anonymous
are we getting to the answer yet
Michele_Laino
  • Michele_Laino
yes! it is a multiplication: \[ \huge - 9x\left( {x - 3} \right) = ...?\]
anonymous
  • anonymous
so whats the final answer
Michele_Laino
  • Michele_Laino
please can you make such computation?
anonymous
  • anonymous
2x^3+3x^2+9x+7x?
Michele_Laino
  • Michele_Laino
no, I'm sorry
anonymous
  • anonymous
which one is it omfg
Michele_Laino
  • Michele_Laino
please continue my computation, we are close to the end
anonymous
  • anonymous
this??????
anonymous
  • anonymous
right?
Michele_Laino
  • Michele_Laino
no, I'm sorry: \[ - 9x\left( {x - 3} \right) = ...?\]
anonymous
  • anonymous
-9x3
Michele_Laino
  • Michele_Laino
it is \(-9x^3+27x\) am I right?
anonymous
  • anonymous
this must be it
anonymous
  • anonymous
dude is it a b c or d you’ve said no to all of them so which on is it
Michele_Laino
  • Michele_Laino
so I update my drawing like below: |dw:1450293966061:dw| oops... it is \(-9x^2+27x\)
anonymous
  • anonymous
what
Michele_Laino
  • Michele_Laino
finally: what is: \[\huge 7x:x\]
anonymous
  • anonymous
7
anonymous
  • anonymous
so this is it
Michele_Laino
  • Michele_Laino
that's right! So we have: |dw:1450294116676:dw| then we have to compute this: \(-7(x-3)=...?\)
anonymous
  • anonymous
okay so last one
anonymous
  • anonymous
Using synthetic division, find (x^4 − 2) ÷ (x + 1).
anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
here we have to apply the same procedure as before
anonymous
  • anonymous
i haven’t really mastered that
anonymous
  • anonymous
so what is it
Michele_Laino
  • 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
  • anonymous
okay thats fine
Michele_Laino
  • Michele_Laino
ok! Now, first step: we have to do this computation: \(x^4:x=...?\)
anonymous
  • anonymous
x^3
Michele_Laino
  • Michele_Laino
right! So I can make this drawing: |dw:1450294494695:dw|
anonymous
  • anonymous
yeah
Michele_Laino
  • Michele_Laino
next, what is: \(-x^3(x+1)=...?\)
anonymous
  • anonymous
-x^4=x^3
anonymous
  • anonymous
i meant - not =
Michele_Laino
  • 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
  • anonymous
-x^2
Michele_Laino
  • Michele_Laino
perfect! So I have this: |dw:1450294775213:dw| now, what is \(x^2(x+1)=...?\)
anonymous
  • anonymous
is this the answer though
Michele_Laino
  • Michele_Laino
I don't know, since I did not such division
anonymous
  • anonymous
x^3+x^2
Michele_Laino
  • Michele_Laino
ok! I update my drawing: |dw:1450294916258:dw| next, what is \(x^2:x=...?\)
anonymous
  • anonymous
x
Michele_Laino
  • Michele_Laino
ok1 So we have: |dw:1450295005204:dw| then, what is \(-x(x+1)=...?\)
Michele_Laino
  • Michele_Laino
oops.. I meant ok!
anonymous
  • anonymous
x+1 sry I’m not sure
Michele_Laino
  • Michele_Laino
it is a multiplication, so we can write this: \(-x(x+1)=-x\cdot x-x\cdot 1=...?\)
anonymous
  • anonymous
ok?
Michele_Laino
  • Michele_Laino
it is \(-x^2-x\) am I right?
anonymous
  • anonymous
yeah i think so
Michele_Laino
  • Michele_Laino
then, I update again my drawing: |dw:1450295269730:dw| now, what is \(-x:x=...?\)
anonymous
  • anonymous
-1
Michele_Laino
  • Michele_Laino
correct! So, I can write this: |dw:1450295356053:dw| finally, what is \(1 \cdot (x+1)=...?\)
anonymous
  • anonymous
x+1?
anonymous
  • anonymous
what is it
anonymous
  • anonymous
I’m a little confused so which on is it exactly?
Michele_Laino
  • 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
  • anonymous
is it a b c or d?
anonymous
  • anonymous
is this it
Michele_Laino
  • 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
  • Michele_Laino
so, what is the right option?
anonymous
  • anonymous
so this is it
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
?
Michele_Laino
  • Michele_Laino
yes! It is option A
anonymous
  • anonymous
YOURE A flutterING MORON I ONLY GOT 2 QUESTIONS RIGHT
anonymous
  • anonymous
WHAT THE ACTUAL flutter
anonymous
  • anonymous
YOU R SO SLOW I WASTED LIKE 3 HOURS ON YOU
anonymous
  • anonymous
EVERYTHING WAS WRONG WTF
anonymous
  • anonymous
OMFG SO DONE
anonymous
  • anonymous
TAKING THE MEDAL BACK
anonymous
  • anonymous
GO flutterING KILL YOURSELF feather
Michele_Laino
  • Michele_Laino
you don't wasted your time, you took your time to master the synthetic division
Nnesha
  • Nnesha
watch your language. plz refrain from offensive language &be respectful.
Nnesha
  • 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
  • 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
  • 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.