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Synthetic Division/ Polynomial Help.........?
Use synthetic division to show that, x = - 5
is the root of the equation, x^3 - 4x^2 - 27x + 90 = 0
Then, use the result to factor the polynomial completely into the form, (x + A) (x + B) (x + C)
Then give the list of values A,B,C that you get.
Thanks for your help!
3 Answers
- RaffaeleLv 79 years agoFavorite Answer
substitute - 5 in the left side of the equation
(-5)^3 - 4(-5)^2 - 27(-5) + 90 = -125 - 4 (25) +135 + 90 = 0
1 - 4 - 27 +90
-5 -5 +45 -90
| 1 -9 +18 | 0
Therefore x^3 - 4x^2 - 27x + 90 = (x + 5)(x^2 - 9x +18)
Apply a similar process with x = 3
1 - 9 18
3 3 -18
1 - 6 | 0
so x^3 - 4x^2 - 27x + 90 = (x + 5)(x - 3)(x - 6)
the values you get are
5
- 3
- 6
- Anonymous9 years ago
-5 . . |||| . .1. . . . -4. . . . . .-27. . . . .90
. . . . . . . . . . . . -5. . . . . . 45. . . . .-90
- - - - - - - - - - - - - - - - - - - - - - - - - - - - (+)
. . . . . . . 1. . . . .-9. . . . . .18. . . . . 0
x^3 - 4x^2 - 27x + 90 = 0
(x^2 - 9x + 18)(x + 5) = 0
(x - 6)(x - 3)(x + 5) = 0
x = -5
or
x = 3
or
x = 6
- mohanrao dLv 79 years ago
-5I1.....- 4......-27 ........90
...........-5........45.........-90
_______________________
... 1......-9.......18..........0
(x^3 - 4x^2 - 27x + 90) = (x + 5)(x^2 - 9x + 18)
=> (x + 5)(x - 6)(x - 3) = 0
A = 5, B = 6 and C = 3
