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can u evaluate f(0) and f(3) ?
What does evaluate mean?
Hmmm hang on. Do you mean put them into the f(X)= thing?
Evaluate means to do this: f(x) = x^3 - 19x + 30 f(0) = (0)^3 - 19(0) + 30 = ? f(3) = (3)^3 - 19(3) + 30 = ?
Yes ok Ill have a go at that and tell you what I got thanks.
Right for f(0) I got 30 and the next one 0
f(3) = 0 Are you sure?
Ill do it again
Did it again and got 0 again.
f(3) = (3)^3 - 19(3) + 30 = 27 - 57 + 30 = 30 + 27 - 57 = 57 - 57 = 0 OK
Yes!! So now I have two more questions. Are you up for helping?
Wait what is the 'hence write down the factor of f(x)' bit?
If you calculated f(3) = 0, then (x-3) is a factor
:) I remeber that now. The 0 ones it is.
(ii) Find p and q such that f(x) = (x-2)(x^2 + px +q). How does one go about this?
(x-2)(x^2 + px +q) = x^3 +px^2 +qx -2x^2 -2px -2q = x^3 +(p-2)x^2 +(q-2p)x - 2q and the orig is x^3 - 19x + 30 so we know that p-2 should be 0 and q-2p should be -19 and -2q should be 30 can you answer now ?
Wait....Where has that big line came from? ohhh you timesed out the brackets! Ok wait a min.
I get it up to when you start saying the so we know p-2=0 bit. I dont know how we know that.
ok you see we have a term (p-2)x^2 but in the general equation we dont have x^2 at all .. so we have to make it disappear .. we do this by saying p-2 = 0