Two of the factors of f(x)=2x^4 - 3x^3 - 7x^2 -8x + 6 are (2x-1) and (x-3). Find another factor. How did do I do this problem?
2007-12-13 02:08:07 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Using synthetic division:-
3 | 2___-3__-7____-8___6
_ |_____6___9____6__- 6
_ |2____3___2___-2___0
Factors are (x - 3)(2x³ + 3x² + 2x - 2)
2x - 1 = 2(x - 1/2)
1/2|2___3___2___-2
__|____1___2____2
__|2___4___4____0
(x - 2)(2x - 1)(x ² + 2x + 2)
2007-12-13 05:25:40 · answer #1 · answered by Como 7 · 2⤊ 0⤋
f(x)=2x^4 - 3x^3 - 7x^2 -8x + 6
divide this equation by 2x-1
the qoutient is x^3-x^2-4x-6 & the reminder is 0
now divide the qoutient with x-3
the qoutient is x^2+2x+2 & the reminder is 0
so the quotient is the 3rd factor
2007-12-13 02:19:49 · answer #2 · answered by Siva 5 · 0⤊ 0⤋
1st do synthetic division with x - 1/2:
1/2 | 2 .. -3 .. -7 .. -8 .. 6
.............. 1 .. -1 .. -4 .. -6
........-------------------------------
....... 2 ... -2 ..-8 .. -12 .. 0
then factor out the 2 and divide by x-3:
3 | 1 .. -1 ..-4 .. -6
........... 3 .. 6 ... 6
....--------------------
.....1 ... 2 .. 2 ...0
so the remaining factor is x² + 2x + 2
2007-12-13 02:29:56 · answer #3 · answered by Philo 7 · 0⤊ 0⤋