If x-1 and x+3 are the factors of x3+10x2+ax+b find a and b

hello : b = - 24 and a = 13

Step-by-step explanation:

let : f (x) = x3+10x2+ax+b

(x - 1) and (x+3) are the factors

so : 1 and - 3 are the zeros of x3+10x2+ax+b

f (1) = 0 and f (-3) = 0

f (1) = 0 : 1^3 + 10 (1) ² + a (1) + b = 0

a + b + 11 = 0 ... (*)

f (-3) = 0 : (-3) ^3 + 10 (-3) ² + a (-3) + b = 0 ... but (-3) ^3 + 10 (-3) ² = - 27+90 = 63

- 3a + b + 63 = 0 ... (**)

(*) - (**); a + b + 11 + 3a - b - 63 = 0

4a = 52

a = 13

subsct (*) in : 13 + b + 11 = 0

b = - 24

second solution: look here