+0  
 
-2
47
2
avatar

For what values of a and b are x+1 and x+2 factors of x^3 - ax^2 - bx - 8?  Write down the other factor.

 Jan 14, 2020
 #1
avatar+340 
+2

for (x+1) and (x+2) be a factor of given polynomialp(x) , they must be its roots. and 

hence according to remainder theorem p(-1) and p(-2) must be 0,

so p(-1)=-1-a+b-8=0

     p(-2)=-8-4a+2b-8=0 

 

solving these 2 simentanous equation.

b-a=9 

b-2a=8

 

so b= 10 and a is 1

 

and polynomial becomes x^3-x^2-10x-8=0 

 

since product of roots is 8(-d/a) and 2 roots are -1 and -2  last root must be 4 so factor is (x-4)

 

you could also go for long division.!!!

cheers 

 Jan 14, 2020
 #2
avatar+20254 
+2

The constant portion of the factors have to multiply to -8

1 x 2 x -4  = -8

the other factor is   x-4

 

multiply it out and you find a = 1  and b=10

 Jan 14, 2020

16 Online Users