Respuesta :

LammettHash
[tex]p(x)=4x^2-5x+6[/tex]

[tex]c=1\implies p(c)=4(1)^2-5(1)+6=5[/tex]

By the remainder theorem, the remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear binomial [tex]x-c[/tex] is equal to [tex]p(c)[/tex]. Via synthetic division, we get

1   |  4   -5   6
.    |        4  -1
- - - - - - - - - - -
.    |  4   -1   5

which translates to

[tex]\dfrac{4x^2-5x+6}{x-1}=4x-1+\dfrac5{x-1}[/tex]

or

[tex]4x^2-5x+6=(4x-1)(x-1)+5[/tex]

Indeed, when [tex]x=1[/tex], the first term on the right hand side vanished and we're left with 5.

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