Question

HELP ME PLEASE!!!!!!

Answer 1

9514 1404 393

Answer:

  -2x +4

Step-by-step explanation:

We can write the polynomial p(x) in terms of the factors (x+2) and (x-3) as ...

  p(x) = (x+2)(x-3)q(x) +ax +b

Where ax+b is the remainder from division by x^2 -x -6 = (x+2)(x-3). The values of 'a' and 'b' can be found from ...

  p(-2) = 8 = -2a +b

  p(3) = -2 = 3a +b

Subtracting the first equation from the second gives ...

  (3a +b) -(-2a +b) = (-2) -(8)

  5a = -10

  a = -2

Then the first equation tells us ...

  8 = -2(-2) +b

  4 = b

So, the remainder from division by (x^2 -x -6) is (-2x +4).