Question

Let f(x) = 6x^3 - tx2 + 7x - 12, where t is a constant such that f(x) is divisible by x - 2

a) Find f(2) in terms of t

b) Find t.

Answer 1

Part a) just evaluate f(x) with x = 2. You'll get an expression in terms of t.

Part b) The Remainder Theorem says that the value of f(c) is the remainder when dividing f(x) by (x-c). But there is no remainder if it is divisible, so we can use the answer from part a to find t by setting it equal to 0 and solving for t.

Answer 2

F(2)=48-4t+14-12
For part A?

Answer 3

correct... now for it be divisible by (x-2).... F(2) must equal 0
48 -4t +14-12 = 0

solve for t