Work out the value of a if when (Algebra 2)

Question

f(x) = ax^3 - 3x^2 + 3x - 3 is divided by (2x-1) the remainder is -2.

Answer 1

According to the remainder theorem, f(1/2) = -2

Therefore a/8 -3/4 +3/2 -3 = -2 solving gives a = 2

This can be checked with synthetic division.

Answer 2

So then f(1/2) = -2 per the remainder theorem

-2 =

f(1/2) = a(1/2)^3 - 3(1/2)^2 + 3(1/2) - 3

= (1/8) a - 3/4 + 3/2 - 3

= (1/8)a -3/4 + 6/4 - 12/4

= (1/8)a - 9/4

-2 = (1/8)a - 9/4

-2 + 9/4 = (1/8) a

MUltiplies everything by 8

-16 +18 = a

a =2

f(x) = 2x^3 - 3x^2 + 3x - 3

Dividing by 2x-1

1/2 | 2 -3 3 -3

1 -1 1

________________________

2 -2 2 -2

a =2