1. ## question

hi i've got a question i'd like some help with:

given that P(x), where $P(x) = x^3 + 3x^2 + kx + 4$ and k is a constant, is such that the remainder on dividing P(x) by $(x - 1)$ is three times the remainder on dividing P(x) by (x + 1), find the value of k

could someone show me the steps to do this please? thankyou

2. Originally Posted by mark
hi i've got a question i'd like some help with:

given that P(x), where $P(x) = x^3 + 3x^2 + kx + 4$ and k is a constant, is such that the remainder on dividing P(x) by $(x - 1)$ is three times the remainder on dividing P(x) by (x + 1), find the value of k

could someone show me the steps to do this please? thankyou
When p(x) is divided by (x - a) the remainder is p(a) (this is something you should already know).

Solve the equation $p(1) = 3 p(-1)$ for k.

3. well i first did P(1) and came up with k = -7 but i'm not sure what to do after that? i tried putting 3p(-1) and seeing what that came up with but didn't seem to make much sense, can someone show me how its done in steps please because i'm lost

4. Originally Posted by mark
well i first did P(1) and came up with k = -7 but i'm not sure what to do after that? i tried putting 3p(-1) and seeing what that came up with but didn't seem to make much sense, can someone show me how its done in steps please because i'm lost
p(1) = 8 + k.

p(-1) = 6 - k.

Substitute these expressions into p(1) = 3 p(-1). Solve for k.

5. ah, 10 = 4k, so its 2.5, thanks