How to Factor x^3 -8x -3

lim (x->3) (x^3 -8x -3)/(x-3)

is the full question,

(x - 3)(x^2 + 3x + 1)/(x - 3) = x^2 + 3x + 1

lim (x->3) (x^3 -8x -3)/(x-3) =

= lim (x->3) ( x^2 + 3x + 1) = 19



P(x) = x^3 - 8x - 3

P(3) = 27 - 24 - 3 = 0

P(x) is divisible by (x - 3)

synthetic division

______1_____0_____-8______-3

___3________3_____9_______3

______1_____3_____1_______0

Q(x) = x^2 + 3x + 1

note: try using the denominator(x-3) as one of the factors of the numerator(x^3-8x-3),

=>(x^3-8x-3) = (x-3)(x^2+3x+1) since you have (x-3) on both the numerator and the denominator cancel it out.

which leaves you with (x^2+3x+1) as the final answer. i hope it helps!

x^3 -8x -3=(x-3)(x^2+3x+1)

lim (x->3)=(x-3)(x^2+3x+1) /(x-3)

lim (x->3)=(x^2+3x+1)

lim=19

dividing the polynomial

we get x^2 + 3x +1

so limit is 9+9+1 = 19