Question

I've included two questions. Hopefully you can help me with both. Thanks!

Answer 1

Answer:

  1.  value is 0; x-3 is a factor . . . . . . . . . . . . . .third choice

  2.  evaluates at x = -1; remainder is -11 . . . . first choice

Step-by-step explanation:

Dividing f(x) by (x -a) gives ...

  f(x)/(x -a) = g(x) +r/(x -a) . . . . some quotient and a remainder r

If we multiply this expression by (x -a), we see ...

  f(x) = (x -a)g(x) +r

so

  f(a) = (a -a)g(a) +r . . . . . evaluate the above equation at x=a

  f(a) = 0 +r

  f(a) = r . . . . . . . . . a statement of the remainder theorem

If r=0, then x-a is a factor of f(x) = (x-a)g(x).

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1. We have "a" = 3, and f(3) = 0. Therefore (x-3) is a factor.

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2. We have "a" = -1, and f(-1) = -11. Therefore the remainder from division by (x+1) is -11.