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.

Guest Jan 14, 2020

#1**+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

kes1968 Jan 14, 2020

#2**+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

ElectricPavlov Jan 14, 2020