anonymous
  • anonymous
plzz help ... Solve each polynomial equation 1. 15x^3-119x^2-10+16=0 2. x^3-14x^2+47x-18=0 3. 5x^3-27x^2-17x-6=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Mertsj
  • Mertsj
I notice that these are all cubics. So I would first try to factor by grouping and if that doesn't work, then try synthetic division.
anonymous
  • anonymous
thank u
anonymous
  • anonymous
how do i do synthetic division with no divisor or watever its called?

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Mertsj
  • Mertsj
Let's look at the first one.. The constant term is 16 and the coefficient of the x^3 term is 15. So the possible rational roots are the factors of 16 over the factors of 15 Use those for your "shelf" numbers in the synthetic division process. If you get a remainder of 0, that number is a root.
Mertsj
  • Mertsj
So the possible rational roots are:\[\pm1, \pm2,\pm4,\pm8,\pm16,\pm1/3,\pm1/5,\pm1/15,\pm2/3,\pm4/3,\pm8/3,\pm16/3,\pm2/5,\pm4/5\]
Mertsj
  • Mertsj
and so on
anonymous
  • anonymous
so i take the numbers and do what?
Mertsj
  • Mertsj
|dw:1327020100318:dw|
Mertsj
  • Mertsj
So we see that 8 is a root and (x-8)(15x^2+x-2) are factors.
Mertsj
  • Mertsj
Take the second factor 15x^2+x-2 and use the quadratic formula on it and find the other roots.
anonymous
  • anonymous
so then the answer is 15x^2-x-2x omg thaks i get it!!!
Mertsj
  • Mertsj
I actually cheated and used a graphing calculator to find the 8
anonymous
  • anonymous
not 2x sorry
Mertsj
  • Mertsj
No that is not the answer. The 3 answers are 8 and whatever you get when you solve 15x^2+x-2=0
anonymous
  • anonymous
ohhh so how do i find that out?
Mertsj
  • Mertsj
Don't you know how to solve a quadratic equation with the quadratic formula?
anonymous
  • anonymous
is that the -b +or - one?
Mertsj
  • Mertsj
yes
anonymous
  • anonymous
sweet i get it now thank you!!!
anonymous
  • anonymous
\[\left\{5 x^3-119 x^2-10 x+16=0,(x-8) (3 x-1) (5 x+2)=0\right\}\left\{x^3-14 x^2+47 x-18=0,(x-9) \left(x^2-5 x+2\right)=0\right\}\left\{5 x^3-27 x^2-17 x-6=0,(x-6) \left(5 x^2+3 x+1\right)=0\right\} \]
Mertsj
  • Mertsj
|dw:1327020932580:dw|
anonymous
  • anonymous
i got for the first one -1|dw:1327021163596:dw|
anonymous
  • anonymous
|dw:1327021250750:dw| this is the answer??
Mertsj
  • Mertsj
Don't you see where I solved it for you?
anonymous
  • anonymous
oh sorry i wasnt looking .. lol
anonymous
  • anonymous
i see it now
Mertsj
  • Mertsj
ok
anonymous
  • anonymous
thanks sooo much
Mertsj
  • Mertsj
yw

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