The factor Theorem? (1 Viewer)

[177152]

*** When f(x)=ax^2 - 3x + 1 and g(x) = x^3 - 3x^2 + 2 are divided by x + 1 the leave the same remainder. Find the value of a. ***

Please help me. I wasn't there when my teacher explained how to do these. I'm lost. I have the test in 4 days and I don't know how to do ones like this.
Thanks. I need the working and solution urgently.

 

[Evergreen]

f(-1) = g(-1)

f(-1)= a+3+1
g(-1)= -1-3+2=-2

.: a+3+1=-2
a=-6

if any function f(x) divided by x+a then the remainder is always f(-a)

in other words replace x with the value of -a and then you have the remainder.

however this rule only applies when the degree of D(x) is 1...i.e a linear function
so you cant apply this rule when dividing a polynomial by say x^2+3x+1.
note: D(x) is the divisor (i.e the expression you are dividing any function P(x) by).

 

[177152]

Thank you very much. I think I know how to do it now. I'll have a good at a few questions and see how I go. Thank you.