# f(x) = ax^3+bx^2-4x-3, where a and b are constants.It is given that (x-1) is a factor of f(x).show that a+b = 7

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`f(x) = ax^3+bx^2-4x-3`

Since (x-1) is a factor we can say f(1) = 0

`f(1) = 0`

`f(1) = a(1)^3+b(1)^2-4xx1-3`

`0 = a+b-7`

`a+b = 7`

*So the requirement is shown.*

*a+b = 7*

f(x)=ax^3+bx^2-4x-3

q(x)=x-1

Remainder= f(1)=0

a*(1)^3+b*(1)^2-4*1-3=0

a+b=4+3

a+b=7. Proved