Use synthtc div to show x=-7 is a root of x^3+7x^2-16x-112=0. Use result to factor polynomial completely in form (x+A)(x+B)(x+C) Give list of values A,B,C

Question

PLease provide the answer (list of values A,B,C). very confused

Answer 1

 

 

-7 |    1   7    -16   -112

 

    ____ -7__  0  __112 ________

 

         1  0    -16      0

 

 

(x+7)(x^2 - 16)

 

(x+7)(x+4)(x-4)

 

So the roots are -7, -4, and 4

 

CHECK:

 

   (-7)^3 + 7(-7)^2 - 16(-7) - 112 = -343 + 343 + 112  - 112  = 0

  (-4)^3 + 7(-4)^2 - 16(-4) - 112 =  -64 + 112 + 64 -112 = 0

  (4)^3 + 7(4)^2 - 16(4) - 112 = 64 + 112 - 64 - 112 = 0