Question

If x - 1 and x + 3 are factors of x³ - ax² - 13x + b, find a and b. Use Factor Theorem for solving the question.
Answer= a = 3, b = 15 in my textbook.
Please solve the complete question.

Answer 1

let g(x) = x³-ax²-13x+b

Since, (x-1) and (x+3) are the factors​ of g(x), then,
g(1)=0 and g(-3)=0.
_______________
g(1)=0
1-a-13+b=0
b-a=12
_______________
g(-3)=0
-27-9a+39+b=0
b-9a=-12
_______________
Now we just have to solve both the equations​.
Subtract both these equations, and you will get a = 3 and b = 15.
b-a=12
b-9a=-12
- - -
8a= 24
a= 3
b =12+a =15

I hope you understand. Do mark it as brainliest if you found it helpful. All the best!