Question

Sorry this a lot.

Answer 1

Your
-4| 3 7 -20
-12 20
______________
3 -5 0
is a bit hard to read.  Try this format:
      __________
-4  /   3    7    -20
              -12   20
      -------------------
         3    -5      0

Because the remainder is 0, we know that -4 is a root and (x+4) is a factor.  Note the new coefficients in the last row:    3   -5.  They are the coeff. of the quotient, namely, 3x-5.  So (3x-5) is a factor of the original polynomial.
      

Answer 2

The correct answers are,

The number -4 is a root of F(x) = 3^x2 + 7x - 20.

(x + 4) is a factor of 3x^2 + 7x - 20.

(3x^2 + 7x - 20) (x + 4) = (3x - 5)