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# Polynomials watch

1. f(x) = x^3 + ax^2 + bx + 8

When f(x) is divided by (x+1), the remainder is 18.
When f(x) is divided by (x-2), the remainder is 0.
Find the values for a and b.

I've put this into a grid and worked out most of it, I'm just missing a value.

Also, I asked on Yahoo and the answer I got was "f(-1) = - 1 + a - b + 8 = 17 & f(2) = 8 + 4a + 2b + 8 = 0---> { 2/3 & - 28 / 3 }" but Id don't understand where the final answer came from.
2. Find f(-1) and f(2) then solve the two simultaneously
3. (Original post by JustJusty)
f(x) = x^3 + ax^2 + bx + 8

When f(x) is divided by (x+1), the remainder is 18.
When f(x) is divided by (x-2), the remainder is 0.
Find the values for a and b.

I've put this into a grid and worked out most of it, I'm just missing a value.

Also, I asked on Yahoo and the answer I got was "f(-1) = - 1 + a - b + 8 = 17 & f(2) = 8 + 4a + 2b + 8 = 0---> { 2/3 & - 28 / 3 }" but Id don't understand where the final answer came from.

my advice would be to leave the "grids" alone and use the remainder/factor theorem
4. (Original post by TeeEm)
my advice would be to leave the "grids" alone and use the remainder/factor theorem
Thanks. As far as I know the answer I was given is using the theorem, I just don't understand the part in the {} brackets. I'v only had the theorem explained very briefly and I didn't even know until now what it's called so I really have no idea what to do.
5. (Original post by JustJusty)
Thanks. As far as I know the answer I was given is using the theorem, I just don't understand the part in the {} brackets. I'v only had the theorem explained very briefly and I didn't even know until now what it's called so I really have no idea what to do.
look at some examples in this link ...
(some questions there are almost identical to yours)
Enlarge to view solution
6. (Original post by TeeEm)
look at some examples in this link ...
7. (Original post by TeeEm)
look at some examples in this link ...
(some questions there are almost identical to yours)
Enlarge to view solution
(Original post by ghostwalker)
sorry busy with my own work ...
here it is
8. Where (x+1)=0, x=-1
Where (x-2)=0, x=2

When you put those numbers into the equation (factor theorem method) you will end up with two separate equations: F(-1) and F(2). The question already tells you the values of these two equations, either by saying it is a factor (or equal to zero) or saying its remainder is a certain number (in this case 18).

So put your equation of F(-1) and F(2) equal to the corresponding value given in the question (unfortunately I'm on mobile and would keep having to switch back and forth).

You'll then have two equations with two unknowns, values A and B.

Now, use a simultaneous equations method - I find substitution can be easiest in these and therefore make you less likely to make mistakes.

Make A the subject of one of your equations (so have one with A= something something) and put whatever A is equal to (in my example, "something something") into the second equation; replacing A.

Then you have one of your equations with just one unknown, value B, and the rest is straight forward rearranging to find B.
Once you find B, substitute it into one of your original equations to find A.
And there you go.

I hope I explained it well enough for it to make sense
Once you do these questions a few times they're as easy as Pi...

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