Question 1108150
1. R(x) =x^3+13x^2+48x+36
 sol 
      x^3+13x^2+48x+36 = 0
put x =-1 we get eqution 0 so first factor is x +1
  dived equation by x+1
     x+1) x^3+13x^2+48x+36( x^2 +12x +36
          x^3+x^2
          _  _
         ________________________
              12x^2 +48x + 36
              12x^2 +12x
             -       -
         ______________________--
                    36x + 36
                    36x + 36
                   -     -
                  _________________
                         0
x^3+13x^2+48x+36 = ( x +1)( x^2 +12x +36)


2. M(x) =3x^4-3x^2

  3x^4-3x^2 = 0
3x^2 ( x^2 -1) =0
3x^2 ( x+1)(x-!)

3. N(x) =x^3+5x^2-8x-12

x^3+5x^2-8x-12 =0
 put x =-1 we get equation 0 so first factor is x +1
  dived equation by x+1

x+1) x^3+5x^2-8x-12 ( x^2 + 4x -12
     x^3+x^2
    -    -
_________________________
         4x^2 -8x -12
         4x^2 +4x
        -     -
_____________________
             -12x - 12
              -12x -12
              +     +
_____________________________
                0


x^3+5x^2-8x-12 = (x+1)(x^2 + 4x -12)
               = (x+1)(x^2 + 6x - 2x -12)
               = (x+1)x(x+6)-2(x+6)
               = (x+1)(x-2)(x+6)

4. P(x) =x^3-8
x^3-8 =0
x^3 - 2^3=0
(x-2)(x^2-2x+4)
5. B(x) =x^4-81
x^4-81 = 0
x^4 - 3^4 = 0
(x^2)^2 - (3^2)^2 =0
(x^2 - 3^2)(x^2 + 3^2) =0
(x+3)(x-3)(x^2 + 9)