given that x-3 is a factor of x^3 + ax^2 + bx - 30 , express a in terms of b .

Answer 1

if x-3 is a factor, then 3 = a root or zero

plug in 3 for x in the 3rd degree polynomial and set it = 0

3^3 + a(3)^2 + b(3) - 30 = 0

27+ 9a +3b -30=0

9a + 3b -3 =0

3a +b-1 =0

b = 1-3a

3a = 1-b

a = (1-b)/3 = 1/3 - b/3

another method is divide x-3 into the 3rd degree polynomial

using either long or synthetic division. You get a remainder of 9a+3b-3. set it equal to zero

and solve for a

9a+3b =3

3a + b = 1

a =1/3 -b/3