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