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You are given that f(x) = x^3 - 19x + 30
1.) Calculate f(0) and f(3). Hence write down a factor of f(x).
Thanks.
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@amistre64 @Hero
mukushla
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can u evaluate f(0) and f(3) ?
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What does evaluate mean?
mukushla
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calculate-compute-
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Hmmm hang on. Do you mean put them into the f(X)= thing?
Hero
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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 = ?
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Yes ok Ill have a go at that and tell you what I got thanks.
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Right for f(0) I got 30 and the next one 0
Hero
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f(3) = 0
Are you sure?
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Ill do it again
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Did it again and got 0 again.
Hero
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f(3) = (3)^3 - 19(3) + 30
= 27 - 57 + 30
= 30 + 27 - 57
= 57 - 57
= 0
OK
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Yes!! So now I have two more questions. Are you up for helping?
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Wait what is the 'hence write down the factor of f(x)' bit?
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@nincompoop
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@estudier
Hero
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If you calculated f(3) = 0, then (x-3) is a factor
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:) I remeber that now. The 0 ones it is.
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(ii) Find p and q such that f(x) = (x-2)(x^2 + px +q). How does one go about this?
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@karatechopper @myininaya
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@Coolsector
Coolsector
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(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 ?
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Wait....Where has that big line came from? ohhh you timesed out the brackets! Ok wait a min.
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I get it up to when you start saying the so we know p-2=0 bit. I dont know how we know that.
Coolsector
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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