Question

solve the equation in the real numbers system: x^4-8x^3+16x^2+8x-17=0

Answer 1

x=1 looks like it might work by inspection
1^4-8*1^3+16*1^2+8(1)-17
=1-8+16+8-17=1+16-17=0
so use syntehic division to find another factor besides (x-1)

Answer 2

1 | 1 -8 16 8 -17
| 1 -7 9 17
--------------------------
1 -7 9 17 | 0
x^3-7x^2+9x+17=0

Answer 3

if it had another rational root it would have to be plus or minus 17. (Rational Root theorem)

Answer 4

-1| 1 -7 9 17
| -1 8 -17
-----------------
1 -8 17| 0

Answer 5

or -1 as well, i always forget that >.<

Answer 6

x=-1 works also

Answer 7

so we have x^2-8x+17=0
we can solve this by using quadratic formula :)
and then we are done

Answer 8

1 | 1 -8 16 8 -17
| 1 -7 9 17
--------------------------
1 -7 9 17 | 0
x^3-7x^2+9x+17=0
i dont really understand about this:(.

Answer 9

how do u got that???

Answer 10

synetic division?

Answer 11

synthetic*

Answer 12

if you want you can also do long division

Answer 13

i dont know with the long division.. ok i'm understanding with the synthetic division now:)