Question

What must be added to (x^3)-3(x^2)-12(x)+19 so that the result is exactly divisible by (x^2)+(x)-6

Answer 1

Hey!!
____________

x²+x-6

=> x²+3x-2x-6

=> x(x+3)-2(x+3)

=> (x-2)(x+3)

now take (x-2)

=> x-2=0

=> x=2

=> p(2)=x³-3x²-12x+19

=> (2)³-3(2)²-12(2)+19

=> 8-12-24+19

=> 27-36

=> -9
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Hope it helps ☺️

Answer 2

x^3-3x^2-12x+19÷x^2+x-6
=x-4 is quotient
=-2x-5 is remainder
Therefore , -2x-5 need to be added




Hope this is helpful for you!!!!!