(2x-1) is a factor of the polynomial 6x^6 + x^5 - 92x^4 + 45x^3 + 184x^2 +4x -48? why?

Answer 1

ok // so plugging in x=1/2 gives the answer, but let's do it the long way

6x^6 + x^5 - 92x^4 + 45x^3 + 184x^2 +4x -48 =
( 2x -1 ) ( 3 x^5 +2 x^4 -45 x^3 + 0 x^2 + 92x +48)

hint // work from higher powers down
(2x-1) ( a x^5 + b x^4 + c x^3 + d x^2 +e x + f ) =
2a x^6 + ( 2b-a)x^5 + (2c-b)x^4 + (2d-c)x^3 +(2e-d)x^2 +(2f-e)x -f
it should be obvious what a, then b, then c, then d, then e, then f must be for 2x-1 to be a factor

Answer 2

Ok, if 2x - 1 is a factor of the polynomial, just replace x = 1/2 on the equation, so if it's cero, then 2x-1 will be a factor.

2x-1 = 0 >>> x = 1/2

Answer 3

The previous answers are crap. But you already knew that.

It is a factor, because when you divide your polynomial by (2x-1) using long division, there is no remainder.

Answer 4

because when you sub in 1/2 for x, the equation equals zero

Answer 5

It reduces the equation into a simpler form.

Answer 6

Because it's the inverse of the numeral outside of the...

"Lassie! What's that, girl? You say Timmy has fallen into the well?"

Answer 7

i bet you made this all up so you would seem smart