Best answer:
−2x³ + 12x² + 8x − 48
First, we'll factor out −2
−2x³ + 12x² + 8x − 48 = −2 (x³ − 6x² − 4x + 24)
According to factor theorem, if f(a) = 0, then (x−a) is a factor of f.
But how do we find value for a?
This is where rational root theorem comes in.
According to rational root theorem, if you have a polynomial...
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Best answer:
−2x³ + 12x² + 8x − 48
First, we'll factor out −2
−2x³ + 12x² + 8x − 48 = −2 (x³ − 6x² − 4x + 24)
According to factor theorem, if f(a) = 0, then (x−a) is a factor of f.
But how do we find value for a?
This is where rational root theorem comes in.
According to rational root theorem, if you have a polynomial function with integer coefficients [x³ − 6x² − 4x + 24], and if the function has rational roots, they will be of the form ±p/q, where p is a factor of constant term (24 ---> p = 1, 2, 3, 4, 6, 8, 12, 24) and q is a factor of leading coefficient (1 ----> q = 1
Possible rational roots: ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
Trying out some of these, we find that x = 2 and x = −2 are both zeros of the polynomial expression, so (x−2) and (x+2) are both factors. Using synthetic division we get:
2 | 1 −6 −4 24
| 2 −8 −24
————————
1 −4 −12 0
−2 | 1 −4 −12
| −2 12
——————
1 −6 0
So remaining factor is (x−6)
−2x³ + 12x² + 8x − 48 = −2 (x−6) (x−2) (x+2)
7 answers
·
Galway
·
1 year ago