+1904 How does x^5-43x^4+720x^3-5800x^2+22000x-30000 equal (x-10)^4*(x-3)? My ti-89 graphic calculator gives this answer when I tell it to factor but I do not know how the ti-89 graphic calculator does it. Anyone who can give me the step-by-step instructions on how to turn x^5-43x^4+720x^3-5800x^2+22000x-30000 to (x-10)^4*(x-3), I would really appreciate it. Please do not work backwards (going from (x-10)^4*(x-3) to x^5-43x^4+720x^3-5800x^2+22000x-30000).
+33616 As it's a fifth-order polynomial there are 5 roots. Call them a, b, c, d and e (not necessarily all different).
The polynomial can be written as: (x-a)(x-b)(x-c)(x-d)(x-e) and this must be the same as your polynomial. Note that if you multiply out the terms in brackets you will end up with the constant term as a*b*c*d*e.
Compare this with the constant term in your polynomial and we see that we must have:
a*b*c*d*e = 30000
Now the factors of 30000 are 24*3*54 which we can rewrite as (2*5)4*3 or 104*3. This is the product of the five numbers 10, 10, 10, 10 and 3, so it's a distinct possibility that we could have a=b=c=d=10 and e=3.
You could then check by multiplying out (x-10)4(x-3) to see if the other terms matched (which they do in this case of course). If they didn't match you could try making five other integers from 24*3*54 .
+33616 As it's a fifth-order polynomial there are 5 roots. Call them a, b, c, d and e (not necessarily all different).
The polynomial can be written as: (x-a)(x-b)(x-c)(x-d)(x-e) and this must be the same as your polynomial. Note that if you multiply out the terms in brackets you will end up with the constant term as a*b*c*d*e.
Compare this with the constant term in your polynomial and we see that we must have:
a*b*c*d*e = 30000
Now the factors of 30000 are 24*3*54 which we can rewrite as (2*5)4*3 or 104*3. This is the product of the five numbers 10, 10, 10, 10 and 3, so it's a distinct possibility that we could have a=b=c=d=10 and e=3.
You could then check by multiplying out (x-10)4(x-3) to see if the other terms matched (which they do in this case of course). If they didn't match you could try making five other integers from 24*3*54 .
