anonymous
  • anonymous
Divide Polynomials? (27x^4-18x^3+9x^2)/3x
Mathematics
schrodinger
  • schrodinger
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Nnesha
  • Nnesha
for long division 5 steps) \(\huge\color{green}{{1:}}\) Divide the first terms \(\huge\color{green}{{2:}}\) multiply(distribute) \(\huge\color{green}{{3:}}\) subtract all terms \(\huge\color{green}{{4:}}\) carry down \(\huge\color{green}{{5:}}\) repeat
anonymous
  • anonymous
can you show me how?
Nnesha
  • Nnesha
|dw:1441648360041:dw|

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Nnesha
  • Nnesha
so divide first terms \[\huge\rm \frac{ 27x^4 }{ 3x } =?\]
anonymous
  • anonymous
9x but what is the exponent rule?
anonymous
  • anonymous
ok page works now. 9x3?
anonymous
  • anonymous
?
Nnesha
  • Nnesha
when we divide same bases we should subtract their exponents or x^4 is same as x times x times x times \[\huge\rm \frac{ 27 ⋅x ⋅x⋅x⋅x }{3⋅x}\]
Nnesha
  • Nnesha
yes that's right now multiply the divisor by 9x^3
Nnesha
  • Nnesha
|dw:1441649011288:dw|
anonymous
  • anonymous
so the final answer is 9x^3+6x^2+3x
Nnesha
  • Nnesha
9x^3 times 3x = 27x^4 and then change the sign first term would cancel out the repeat those steps |dw:1441649027500:dw|
Nnesha
  • Nnesha
show ur work plz :=0
Nnesha
  • Nnesha
:=)*
anonymous
  • anonymous
Ok I see! Thanks!!! I assume multiplying is adding exponents so just the division in reverse?
Nnesha
  • Nnesha
yes right!
anonymous
  • anonymous
thank you!
Nnesha
  • Nnesha
multiply same bases `ADD` exponents \[\rm x^m \times x^n =x^{m+n}\] divide same bases `subtract` exponents \[\rm \frac{ x^m }{x^n }=x^{m-n}\]
Nnesha
  • Nnesha
yw!
anonymous
  • anonymous
btw, what if there's more after the variable in the divisor. say 3x-2?
Nnesha
  • Nnesha
then you have to multiply by both terms like 9x^3(3x-2) 9x^3 times 3x - 9x^3 times -2
anonymous
  • anonymous
what would 9x^3 times -2 look like
Nnesha
  • Nnesha
lets say |dw:1441649570148:dw|there is 3x-2
Nnesha
  • Nnesha
just multiply the coefficients\[\huge\rm -9x^3 \times -2=(-9 \times -2)x^3\]
anonymous
  • anonymous
oh so just 18x3
Nnesha
  • Nnesha
yes right!
anonymous
  • anonymous
but where do you go from there? how does it get to the next step?
Nnesha
  • Nnesha
just repeat the steps divide first terms multiply the result by the divisor change signs
anonymous
  • anonymous
but what's the point of the -2 then? idk im confused. i guess where do you put the 18x3?
Nnesha
  • Nnesha
below the 2nd term
Nnesha
  • Nnesha
coefficients should be the same so 9x^3 times -2 = -18x^3 <--3rd degree so put under the x^3 term
anonymous
  • anonymous
oh i see, it cancels out? so it's 9x^2 / 3x-2 now?
anonymous
  • anonymous
ok i think i got it now.
Nnesha
  • Nnesha
no just divide first terms !
Nnesha
  • Nnesha
first term of polynomial by first term of divisor so it would be \[\huge\rm \frac{ 9x^2 }{ 3x }\]
anonymous
  • anonymous
ok give me a second
Nnesha
  • Nnesha
ok!
anonymous
  • anonymous
i have to go be back in a while
Nnesha
  • Nnesha
alright same here cya
anonymous
  • anonymous
@nnesha are you still here? ok i was using 9x^3 as an example. the real problem is 6x^3+11x^2-4x-4 / 3x-2
Nnesha
  • Nnesha
same steps ;=)
Nnesha
  • Nnesha
so first terms are 6x^3 and first term of divisor is 3x divide 6x^3/3x

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