Given that when f(x) is divided by (x-1) the remainder is 4, find the value of b if a is 3.

Question

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

given that when f(x) is divided by (x-1) the remainder is 4, find the value of b if a is 3. 

Answer 1

b=-1

(x-1)(3x^2+2x+1) = 3x^3-x^2-x-1, remainder 4 adds 4 to get 3x^3-x^2-x+3

use long or synthetic division, remainder = 6+2b = 4, b=-1

Answer 2

Using the remainder theorem; we know that the remainder of the polynomial division is equivalent to the value of f for that x.

In this case...when f(x) is divided by (x - 1) the remainder is 4. This means that f(1) must equal 4!

Start by substituting 1 everywhere there is an x, and of course putting the 3 in for a.

3(1)³ + b(1)² + b(1) + 3 this must equal 4.....remember f(1) = 4

3 + b + b + 3 = 4

2b + 6 = 4

b = -1