Question

what must be added to x3 - 3x2 - 12x + 19 so that the result is exactly divisible by x2 + x -6 ?

Answer 1

WELCOME TO OPENSTUDY!! :D

Answer 2

divide dem both

Answer 3

Is it your question ?:
3x - 6 - 12x +19 ?
If we have that can write it :
-9x+9
And can write the 2th sentence this :
3x-6
Now we should reduce the 2th from 1th sentence .
It s :
3x-6-(-9x+9)=3x-6+9x-9=12x-15
Understand?!:)

Answer 4

@E.ali
dude u had interpreted wrongly

actually question is x^3-3x^2-12x+19 -------------equation 1

x^2+x-6 --------equation 2


@queen151999

Ans will be equation 1 / equation 2 which will be equal to -2x-5

Answer 5

No, not quite. The question is:

if f(x)= \(x^3-3x^2-12x+19 \)
& g(x)=\(x^2+x-6 \)

then what must be ADDED to f(x) so that the division f(x)/g(x) has NO remainder?

Answer 6

since \(x^2+x-6 =(x+3)(x-2)\), those will both need to be factors of the revised f(x) when you're finished with it.

Answer 7

I think the idea is just to find a factor (x-a) so that

\((x+3)(x-2)(x-a)=x^3-3x^2-12x+19+h(x)\)

The easiest way is just to pick an a, find that product, and then see what you need to add to \(x^3-3x^2-12x+19\) to GET that. Whatever you have to add, that will be your h(x).

Answer 8

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