1.

If ( x+1) and (x-2)are factors of x^3+(a+1)x^2- (b-2)x -6, find the values of a and b. And then, factories the expression completely.​

Answer»

Answer:

a=2, B=6

Step-by-step EXPLANATION:

X=-1 and x=2

p(x)=x³+ (a+1)x²-(b-2)x-6

p(-1)=(-1)³+(a+1)-1²-(b-2)-1-6

     =-1+(a+1)1-(-b+2)-6

     =-1+a+1+b-2-6

     0=a+b-8

      a+b=8

      a=8-b-------------------------a

p(2)=(2)³+(a+1)2²-(b-2)2-6

     =8+(a+1)4-(b-2)2-6

     =8+4a+4-(2b-4)-6

     =8+4a+4-2b+4-6

     =4a-2b+10

 0=4a-2b+10

4a+2b=-10

a=-10-2b/4-------------------------b

equate 'a' and 'b':

8-b=10-2b/4

cross multiply,

   4(8-b)=-10-2b

   32-4b=-10-2b

   32+10=-2b+4b

   42=2b

   b=6

 subsitute b in a,

a=8-b

 = 8-6

   a=2

   


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